SweetStudy (HomeworkMarket.com)
  • chat0

MULTIPLE CHOICE QUESTIONS (MCQS) ON INTEGRATION OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS WITH ANSWERS INTEGRATION OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS

Is there anything else you׳d like to ask?
Our top-rated tutors can help you.

Click here to post a question
Related Documents
1 / 66100%
MULTIPLE CHOICE QUESTIONS (MCQS) ON INTEGRATION OF
EXPONENTIAL AND LOGARITHMIC FUNCTIONS WITH ANSWERS:
INTEGRATION OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS
1. ∫ e^x dx = ?
a) e^x + C
b) e^x
c) ln|x| + C
d) x e^x + C
Answer: a) e^x + C
2. ∫ e^(2x) dx = ?
a) e^(2x) + C
b) 1/2 e^(2x) + C
c) 2e^(2x) + C
d) e^x + C
Answer: b) 1/2 e^(2x) + C
3. ∫ x e^x dx = ?
a) e^x + C
b) x e^x + C
c) e^x (x - 1) + C
d) e^x (x + 1) + C
Answer: c) e^x (x - 1) + C
4. ∫ ln(x) dx = ?
a) x ln(x) + C
b) x ln(x) - x + C
c) ln(x) + C
d) x/ln(x) + C
Answer: b) x ln(x) - x + C
5. ∫ x ln(x) dx = ?
a) 1/2 x^2 ln(x) - 1/4 x^2 + C
b) 1/2 x^2 ln(x) + C
c) x^2 ln(x) - x + C
d) x^2 ln(x) - x^2 + C
Answer: a) 1/2 x^2 ln(x) - 1/4 x^2 + C
6. ∫ e^(3x) dx = ?
a) 1/3 e^(3x) + C
b) 3 e^(3x) + C
c) e^(3x) + C
d) 1/9 e^(3x) + C
Answer: a) 1/3 e^(3x) + C
7. ∫ ln(2x) dx = ?
a) x ln(2x) + C
b) x ln(2x) - x + C
c) 2x ln(2x) - 2x + C
d) 2x ln(x) - x + C
Answer: b) x ln(2x) - x + C
8. ∫ e^(-x) dx = ?
a) -e^(-x) + C
b) e^(-x) + C
c) -e^x + C
d) ln|x| + C
Answer: a) -e^(-x) + C
9. ∫ x^2 e^x dx = ?
a) e^x (x^2 - 2x + 2) + C
b) e^x (x^2 + 2x + 2) + C
c) e^x (x^2 - 2) + C
d) e^x (x^2 - 2x - 2) + C
Answer: a) e^x (x^2 - 2x + 2) + C
10. ∫ ln^2(x) dx = ?
a) x ln^2(x) - 2x ln(x) + 2x + C
b) x ln^2(x) - x + C
c) x^2 ln^2(x) - 2x + C
d) x ln^2(x) - 2x + C
Answer: a) x ln^2(x) - 2x ln(x) + 2x + C
11. ∫ e^(x^2) dx = ?
a) 1/2 e^(x^2) + C
b) x e^(x^2) + C
c) Cannot be expressed in terms of elementary functions
d) e^(x^2/2) + C
Answer: c) Cannot be expressed in terms of elementary functions
12. ∫ ln(x^2) dx = ?
a) x ln(x^2) - 2x + C
b) 2x ln(x) - 2x + C
c) x^2 ln(x^2) - x^2 + C
d) 2x ln(x^2) - x + C
Answer: b) 2x ln(x) - 2x + C
13. ∫ e^(2x+1) dx = ?
a) 1/2 e^(2x+1) + C
b) e^(2x+1) + C
c) 2 e^(2x+1) + C
d) e^(2x) + e + C
Answer: a) 1/2 e^(2x+1) + C
14. ∫ ln(e^x) dx = ?
a) e^x + C
b) x^2/2 + C
c) x ln(x) - x + C
d) ln(x) + C
Answer: b) x^2/2 + C
15. ∫ x e^(2x) dx = ?
a) 1/2 x e^(2x) - 1/4 e^(2x) + C
b) 1/2 e^(2x) (x - 1/2) + C
c) e^(2x) (x - 1/2) + C
d) 1/2 x^2 e^(2x) + C
Answer: b) 1/2 e^(2x) (x - 1/2) + C
16. ∫ ln(1/x) dx = ?
a) -x ln(x) - x + C
b) x ln(1/x) - x + C
c) -ln(x) + C
d) 1/x + C
Answer: a) -x ln(x) - x + C
17. ∫ e^(ax) dx = ? (where a is a constant, a ≠ 0)
a) 1/a e^(ax) + C
b) a e^(ax) + C
c) e^(ax) + C
d) ln|a| e^(ax) + C
Answer: a) 1/a e^(ax) + C
18. ∫ ln(x+1) dx = ?
a) x ln(x+1) - x + C
b) (x+1) ln(x+1) - x + C
c) x ln(x+1) + C
d) (x+1) ln(x+1) - (x+1) + C
Answer: d) (x+1) ln(x+1) - (x+1) + C
19. ∫ x^2 ln(x) dx = ?
a) 1/3 x^3 ln(x) - 1/9 x^3 + C
b) 1/3 x^3 ln(x) - 1/3 x^3 + C
c) x^3 ln(x) - x^2 + C
d) x^2 ln(x) - 2x + C
Answer: a) 1/3 x^3 ln(x) - 1/9 x^3 + C
20. ∫ e^(sin x) dx = ?
a) -cos(x) e^(sin x) + C
b) sin(x) e^(sin x) + C
c) Cannot be expressed in terms of elementary functions
d) e^(sin x) + C
Answer: c) Cannot be expressed in terms of elementary functions
21. ∫ ln(cos x) dx = ?
a) x ln(cos x) - x tan(x) + C
b) sin(x) ln(cos x) + x + C
c) x ln(cos x) + sin(x) + C
d) x ln(cos x) - sin(x) + C
Answer: c) x ln(cos x) - sin(x) + C
22. ∫ e^(x^3) dx = ?
a) 1/3 e^(x^3) + C
b) x e^(x^3) + C
c) Cannot be expressed in terms of elementary functions
d) e^(x^3/3) + C
Answer: c) Cannot be expressed in terms of elementary functions
23. ∫ ln(tan x) dx = ?
a) x ln(tan x) - x + C
b) x ln(sin x) - x ln(cos x) + C
c) tan(x) ln(tan x) - tan(x) + C
d) sin(x) ln(tan x) + cos(x) + C
Answer: b) x ln(sin x) - x ln(cos x) + C
24. ∫ e^(1/x) dx = ?
a) x e^(1/x) + C
b) e^(1/x) + C
c) Cannot be expressed in terms of elementary functions
d) ln|x| e^(1/x) + C
Answer: c) Cannot be expressed in terms of elementary functions
25. ∫ ln(x) / x dx = ?
a) ln(ln|x|) + C
b) ln^2(x) / 2 + C
c) x ln(x) - x + C
d) ln(x) + C
Answer: b) ln^2(x) / 2 + C
26. ∫ e^(2x) sin(x) dx = ?
a) 1/5 e^(2x) (2 sin(x) - cos(x)) + C
b) 1/5 e^(2x) (2 cos(x) + sin(x)) + C
c) 1/5 e^(2x) (2 sin(x) + cos(x)) + C
d) 1/5 e^(2x) (sin(x) - 2 cos(x)) + C
Answer: a) 1/5 e^(2x) (2 sin(x) - cos(x)) + C
27. ∫ ln(x^2 + 1) dx = ?
a) x ln(x^2 + 1) - 2x + 2 tan^(-1)(x) + C
b) x ln(x^2 + 1) - x + tan^(-1)(x) + C
c) 2x ln(x^2 + 1) - 2x + C
d) x ln(x^2 + 1) - 2x + C
Answer: a) x ln(x^2 + 1) - 2x + 2 tan^(-1)(x) + C
28. ∫ e^(x) cos(x) dx = ?
a) 1/2 e^x (sin(x) + cos(x)) + C
b) 1/2 e^x (sin(x) - cos(x)) + C
c) e^x cos(x) + C
d) e^x sin(x) + C
Answer: a) 1/2 e^x (sin(x) + cos(x)) + C
29. ∫ ln(sin x) dx = ?
a) x ln(sin x) + cos(x) + C
b) sin(x) ln(sin x) - sin(x) + C
c) x ln(sin x) - x + C
d) x ln(sin x) - cos(x) + C
Answer: a) x ln(sin x) + cos(x) + C
30. ∫ e^(ax) sin(bx) dx = ? (where a and b are constants, a^2 + b^2 ≠ 0)
a) e^(ax) (a sin(bx) - b cos(bx)) / (a^2 + b^2) + C
b) e^(ax) (a sin(bx) + b cos(bx)) / (a^2 + b^2) + C
c) e^(ax) (b sin(bx) - a cos(bx)) / (a^2 + b^2) + C
d) e^(ax) sin(bx) / (a + b) + C
Answer: c) e^(ax) (b sin(bx) - a cos(bx)) / (a^2 + b^2) + C
31. ∫ ln(sec x) dx = ?
a) x ln(sec x) - ln|tan x + sec x| + C
b) sec(x) ln(sec x) - tan(x) + C
c) x ln(sec x) + tan(x) + C
d) ln(tan(x/2 + π/4)) + C
Answer: a) x ln(sec x) - ln|tan x + sec x| + C
32. ∫ e^(x^2/2) dx = ?
a) x e^(x^2/2) + C
b) e^(x^2/4) + C
c) Cannot be expressed in terms of elementary functions
d) √(π/2) erf(x/√2) + C
Answer: c) Cannot be expressed in terms of elementary functions
33. ∫ ln(x) / (1 + x^2) dx = ?
a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
b) ln(1 + x^2) / 2 + C
c) x ln(x) / (1 + x^2) + C
d) ln(x) arctan(x) + C
Answer: a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
34. ∫ e^(sin x) cos(x) dx = ?
a) e^(sin x) + C
b) -e^(sin x) + C
c) cos(x) e^(sin x) + C
d) sin(x) e^(sin x) + C
Answer: a) e^(sin x) + C
35. ∫ ln(x + √(x^2 + 1)) dx = ?
a) x ln(x + √(x^2 + 1)) - √(x^2 + 1) + C
b) √(x^2 + 1) + C
c) x ln(x + √(x^2 + 1)) + C
d) ln(x + √(x^2 + 1)) + x + C
Answer: a) x ln(x + √(x^2 + 1)) - √(x^2 + 1) + C
36. ∫ e^(1/x^2) dx = ?
a) x e^(1/x^2) + C
b) -1/2 x e^(1/x^2) + C
c) Cannot be expressed in terms of elementary functions
d) e^(1/x^2) / x + C
Answer: c) Cannot be expressed in terms of elementary functions
37. ∫ ln(tan x) sec^2 x dx = ?
a) ln|sec x| + C
b) tan(x) ln(tan x) + C
c) sec(x) ln(tan x) + C
d) ln(sin x) - ln(cos x) + C
Answer: a) ln|sec x| + C
38. ∫ e^(x) ln(x) dx = ?
a) e^x ln(x) - e^x + C
b) x e^x ln(x) + C
c) e^x (ln(x) - 1) + C
d) e^x ln(x) + x + C
Answer: c) e^x (ln(x) - 1) + C
39. ∫ ln(x) / √(1 - x^2) dx = ?
a) π ln((1 + √(1 - x^2)) / x) + C
b) arcsin(x) ln(x) + C
c) √(1 - x^2) ln(x) + C
d) x ln(x) / √(1 - x^2) + C
Answer: b) arcsin(x) ln(x) + C
40. ∫ e^(tan x) sec^2 x dx = ?
a) e^(tan x) + C
b) tan(x) e^(tan x) + C
c) sec(x) e^(tan x) + C
d) e^(sec x) + C
Answer: a) e^(tan x) + C
41. ∫ ln(cos x) sin x dx = ?
a) -ln(cos x) cos x + C
b) ln(cos x) cos x + C
c) -sin(x) ln(cos x) + C
d) cos(x) ln(cos x) - x + C
Answer: b) ln(cos x) cos x + C
42. ∫ e^(x^2) x dx = ?
a) 1/2 e^(x^2) + C
b) x e^(x^2) + C
c) e^(x^2/2) + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/2 e^(x^2) + C
43. ∫ ln(x^2 - 1) dx = ?
a) x ln(x^2 - 1) - 2x + 2 ln(x + 1) + C
b) x ln(x^2 - 1) - 2x + C
c) (x^2 - 1) ln(x^2 - 1) - x^2 + C
d) x ln(x^2 - 1) - x + C
Answer: b) x ln(x^2 - 1) - 2x + C
44. ∫ e^(sin x) sin x dx = ?
a) -e^(sin x) cos x + C
b) e^(sin x) + C
c) e^(sin x) sin x + C
d) -e^(sin x) + C
Answer: d) -e^(sin x) + C
45. ∫ ln(x) / x^2 dx = ?
a) -ln(x) / x - 1/x + C
b) -1 / (x ln(x)) + C
c) ln^2(x) / 2x + C
d) -ln(x) / x + C
Answer: a) -ln(x) / x - 1/x + C
46. ∫ e^(1/x) / x^2 dx = ?
a) -e^(1/x) / x + C
b) e^(1/x) / x + C
c) -e^(1/x) + C
d) e^(1/x) + C
Answer: a) -e^(1/x) / x + C
47. ∫ ln(sin x) cos x dx = ?
a) sin(x) ln(sin x) + cos(x) + C
b) sin(x) ln(sin x) - x + C
c) cos(x) ln(sin x) + sin(x) + C
d) sin(x) ln(sin x) + C
Answer: a) sin(x) ln(sin x) + cos(x) + C
48. ∫ e^(x) ln(x) dx = ?
a) e^x ln(x) - Ei(x) + C
b) x e^x ln(x) + C
c) e^x (ln(x) - 1) + C
d) e^x ln(x) + x + C
Answer: a) e^x ln(x) - Ei(x) + C
49. ∫ ln(1 + e^x) dx = ?
a) x ln(1 + e^x) - Li_2(-e^x) + C
b) (1 + e^x) ln(1 + e^x) - e^x + C
c) x ln(1 + e^x) - x + C
d) e^x ln(1 + e^x) + C
Answer: a) x ln(1 + e^x) - Li_2(-e^x) + C
50. ∫ e^(a ln x) dx = ? (where a is a constant, a ≠ -1)
a) x^(a+1) / (a+1) + C
b) e^(a ln x) / a + C
c) ln(x^a) + C
d) x^a + C
Answer: a) x^(a+1) / (a+1) + C
51. ∫ ln(x + √(x^2 + a^2)) dx = ? (where a is a constant)
a) x ln(x + √(x^2 + a^2)) - √(x^2 + a^2) + C
b) (x + √(x^2 + a^2)) ln(x + √(x^2 + a^2)) - x + C
c) x ln(x + √(x^2 + a^2)) - x + a arcsinh(x/a) + C
d) ln(x + √(x^2 + a^2)) √(x^2 + a^2) + C
Answer: c) x ln(x + √(x^2 + a^2)) - x + a arcsinh(x/a) + C
52. ∫ e^(ax) cos(bx) dx = ? (where a and b are constants, a^2 + b^2 ≠ 0)
a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
b) e^(ax) (a cos(bx) - b sin(bx)) / (a^2 + b^2) + C
c) e^(ax) cos(bx) / (a + b) + C
d) e^(ax) (b cos(bx) - a sin(bx)) / (a^2 + b^2) + C
Answer: a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
53. ∫ ln(sec x + tan x) dx = ?
a) x ln(sec x + tan x) - x + C
b) ln|sec x + tan x| + C
c) sec x ln(sec x + tan x) + C
d) tan x + C
Answer: b) ln|sec x + tan x| + C
54. ∫ e^(x^2) erf(x) dx = ?
a) 1/2 e^(x^2) erf(x) + C
b) erf(x) / 2 + C
c) Cannot be expressed in terms of elementary functions
d) e^(x^2) + C
Answer: a) 1/2 e^(x^2) erf(x) + C
55. ∫ ln(x) / (x^2 + 1) dx = ?
a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
b) ln(x^2 + 1) / 2 - arctan(x) + C
c) x ln(x) / (x^2 + 1) + C
d) ln(x) arctan(x) + C
Answer: a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
56. ∫ e^(x^2) x^2 dx = ?
a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
b) 1/2 e^(x^2) + C
c) x^3 e^(x^2) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
57. ∫ ln(cosh x) dx = ?
a) x ln(cosh x) - sinh x + C
b) sinh x ln(cosh x) + C
c) x ln(cosh x) - x + C
d) cosh x ln(cosh x) - sinh x + C
Answer: a) x ln(cosh x) - sinh x + C
58. ∫ e^(sin x) sin x dx = ?
a) -e^(sin x) cos x + C
b) e^(sin x) + C
c) e^(sin x) sin x + C
d) -e^(sin x) + C
Answer: b) e^(sin x) + C
59. ∫ ln(x^2 + a^2) dx = ? (where a is a constant)
a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
b) 2x ln(x^2 + a^2) - 2x + C
c) x ln(x^2 + a^2) - x + a arctan(x/a) + C
d) (x^2 + a^2) ln(x^2 + a^2) - x^2 + C
Answer: a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
60. ∫ e^(ax^2) x dx = ? (where a is a constant, a ≠ 0)
a) 1/(2a) e^(ax^2) + C
b) x e^(ax^2) + C
c) e^(ax^2/2) + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/(2a) e^(ax^2) + C
61. ∫ ln(tan(x/2)) dx = ?
a) 2 ln|sec(x/2)| + C
b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
c) 2 ln|sin(x/2)| + C
d) tan(x/2) ln(tan(x/2)) + C
Answer: b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
62. ∫ e^(1/sin x) csc^2 x dx = ?
a) -e^(1/sin x) cot x + C
b) e^(1/sin x) + C
c) -e^(1/sin x) + C
d) e^(1/sin x) csc x + C
Answer: c) -e^(1/sin x) + C
63. ∫ ln(x + √(x^2 - 1)) dx = ?
a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
b) √(x^2 - 1) + C
c) x ln(x + √(x^2 - 1)) + C
d) ln(x + √(x^2 - 1)) + x + C
Answer: a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
64. ∫ e^(arcsin x) / √(1 - x^2) dx = ?
a) e^(arcsin x) + C
b) arcsin(x) e^(arcsin x) + C
c) x e^(arcsin x) + C
d) √(1 - x^2) e^(arcsin x) + C
Answer: a) e^(arcsin x) + C
65. ∫ ln(1 - x^2) dx = ?
a) x ln(1 - x^2) + 2x + C
b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
c) (1 - x^2) ln(1 - x^2) + x^2 + C
d) x ln(1 - x^2) - 2x + C
Answer: b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
66. ∫ e^(cos x) sin x dx = ?
a) -e^(cos x) + C
b) e^(cos x) + C
c) e^(cos x) sin x + C
d) -e^(cos x) cos x + C
Answer: a) -e^(cos x) + C
67. ∫ ln(x) √(1 - x^2) dx = ?
a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
b) x ln(x) √(1 - x^2) + C
c) ln(x) arcsin(x) + C
d) √(1 - x^2) ln(x) - x + C
Answer: a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
68. ∫ e^(x^3) x^2 dx = ?
a) 1/3 e^(x^3) + C
b) x e^(x^3) + C
c) e^(x^3) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/3 e^(x^3) + C
69. ∫ ln(sec x + tan x) sec x dx = ?
a) ln|sec x + tan x| + C
b) tan x ln(sec x + tan x) + C
c) sec x ln(sec x + tan x) + C
d) ln(sec x + tan x) + tan x + C
Answer: c) sec x ln(sec x + tan x) + C
70. ∫ e^(1/x) / x dx = ?
a) e^(1/x) + C
b) ln|x| e^(1/x) + C
c) Cannot be expressed in terms of elementary functions
d) -Ei(-1/x) + C
Answer: c) Cannot be expressed in terms of elementary functions
71. ∫ ln(x) / (1 - x^2) dx = ?
a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
b) ln(x) / √(1 - x^2) + C
c) arcsin(x) ln(x) + C
d) x ln(x) / (1 - x^2) + C
Answer: a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
52. ∫ e^(ax) cos(bx) dx = ? (where a and b are constants, a^2 + b^2 ≠ 0)
a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
b) e^(ax) (a cos(bx) - b sin(bx)) / (a^2 + b^2) + C
c) e^(ax) cos(bx) / (a + b) + C
d) e^(ax) (b cos(bx) - a sin(bx)) / (a^2 + b^2) + C
Answer: a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
53. ∫ ln(sec x + tan x) dx = ?
a) x ln(sec x + tan x) - x + C
b) ln|sec x + tan x| + C
c) sec x ln(sec x + tan x) + C
d) tan x + C
Answer: b) ln|sec x + tan x| + C
54. ∫ e^(x^2) erf(x) dx = ?
a) 1/2 e^(x^2) erf(x) + C
b) erf(x) / 2 + C
c) Cannot be expressed in terms of elementary functions
d) e^(x^2) + C
Answer: a) 1/2 e^(x^2) erf(x) + C
55. ∫ ln(x) / (x^2 + 1) dx = ?
a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
b) ln(x^2 + 1) / 2 - arctan(x) + C
c) x ln(x) / (x^2 + 1) + C
d) ln(x) arctan(x) + C
Answer: a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
56. ∫ e^(x^2) x^2 dx = ?
a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
b) 1/2 e^(x^2) + C
c) x^3 e^(x^2) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
57. ∫ ln(cosh x) dx = ?
a) x ln(cosh x) - sinh x + C
b) sinh x ln(cosh x) + C
c) x ln(cosh x) - x + C
d) cosh x ln(cosh x) - sinh x + C
Answer: a) x ln(cosh x) - sinh x + C
58. ∫ e^(sin x) sin x dx = ?
a) -e^(sin x) cos x + C
b) e^(sin x) + C
c) e^(sin x) sin x + C
d) -e^(sin x) + C
Answer: b) e^(sin x) + C
59. ∫ ln(x^2 + a^2) dx = ? (where a is a constant)
a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
b) 2x ln(x^2 + a^2) - 2x + C
c) x ln(x^2 + a^2) - x + a arctan(x/a) + C
d) (x^2 + a^2) ln(x^2 + a^2) - x^2 + C
Answer: a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
60. ∫ e^(ax^2) x dx = ? (where a is a constant, a ≠ 0)
a) 1/(2a) e^(ax^2) + C
b) x e^(ax^2) + C
c) e^(ax^2/2) + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/(2a) e^(ax^2) + C
61. ∫ ln(tan(x/2)) dx = ?
a) 2 ln|sec(x/2)| + C
b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
c) 2 ln|sin(x/2)| + C
d) tan(x/2) ln(tan(x/2)) + C
Answer: b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
62. ∫ e^(1/sin x) csc^2 x dx = ?
a) -e^(1/sin x) cot x + C
b) e^(1/sin x) + C
c) -e^(1/sin x) + C
d) e^(1/sin x) csc x + C
Answer: c) -e^(1/sin x) + C
63. ∫ ln(x + √(x^2 - 1)) dx = ?
a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
b) √(x^2 - 1) + C
c) x ln(x + √(x^2 - 1)) + C
d) ln(x + √(x^2 - 1)) + x + C
Answer: a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
64. ∫ e^(arcsin x) / √(1 - x^2) dx = ?
a) e^(arcsin x) + C
b) arcsin(x) e^(arcsin x) + C
c) x e^(arcsin x) + C
d) √(1 - x^2) e^(arcsin x) + C
Answer: a) e^(arcsin x) + C
65. ∫ ln(1 - x^2) dx = ?
a) x ln(1 - x^2) + 2x + C
b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
c) (1 - x^2) ln(1 - x^2) + x^2 + C
d) x ln(1 - x^2) - 2x + C
Answer: b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
66. ∫ e^(cos x) sin x dx = ?
a) -e^(cos x) + C
b) e^(cos x) + C
c) e^(cos x) sin x + C
d) -e^(cos x) cos x + C
Answer: a) -e^(cos x) + C
67. ∫ ln(x) √(1 - x^2) dx = ?
a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
b) x ln(x) √(1 - x^2) + C
c) ln(x) arcsin(x) + C
d) √(1 - x^2) ln(x) - x + C
Answer: a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
68. ∫ e^(x^3) x^2 dx = ?
a) 1/3 e^(x^3) + C
b) x e^(x^3) + C
c) e^(x^3) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/3 e^(x^3) + C
69. ∫ ln(sec x + tan x) sec x dx = ?
a) ln|sec x + tan x| + C
b) tan x ln(sec x + tan x) + C
c) sec x ln(sec x + tan x) + C
d) ln(sec x + tan x) + tan x + C
Answer: c) sec x ln(sec x + tan x) + C
70. ∫ e^(1/x) / x dx = ?
a) e^(1/x) + C
b) ln|x| e^(1/x) + C
c) Cannot be expressed in terms of elementary functions
d) -Ei(-1/x) + C
Answer: c) Cannot be expressed in terms of elementary functions
71. ∫ ln(x) / (1 - x^2) dx = ?
a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
b) ln(x) / √(1 - x^2) + C
c) arcsin(x) ln(x) + C
d) x ln(x) / (1 - x^2) + C
Answer: a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
52. ∫ e^(ax) cos(bx) dx = ? (where a and b are constants, a^2 + b^2 ≠ 0)
a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
b) e^(ax) (a cos(bx) - b sin(bx)) / (a^2 + b^2) + C
c) e^(ax) cos(bx) / (a + b) + C
d) e^(ax) (b cos(bx) - a sin(bx)) / (a^2 + b^2) + C
Answer: a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
53. ∫ ln(sec x + tan x) dx = ?
a) x ln(sec x + tan x) - x + C
b) ln|sec x + tan x| + C
c) sec x ln(sec x + tan x) + C
d) tan x + C
Answer: b) ln|sec x + tan x| + C
54. ∫ e^(x^2) erf(x) dx = ?
a) 1/2 e^(x^2) erf(x) + C
b) erf(x) / 2 + C
c) Cannot be expressed in terms of elementary functions
d) e^(x^2) + C
Answer: a) 1/2 e^(x^2) erf(x) + C
55. ∫ ln(x) / (x^2 + 1) dx = ?
a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
b) ln(x^2 + 1) / 2 - arctan(x) + C
c) x ln(x) / (x^2 + 1) + C
d) ln(x) arctan(x) + C
Answer: a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
56. ∫ e^(x^2) x^2 dx = ?
a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
b) 1/2 e^(x^2) + C
c) x^3 e^(x^2) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
57. ∫ ln(cosh x) dx = ?
a) x ln(cosh x) - sinh x + C
b) sinh x ln(cosh x) + C
c) x ln(cosh x) - x + C
d) cosh x ln(cosh x) - sinh x + C
Answer: a) x ln(cosh x) - sinh x + C
58. ∫ e^(sin x) sin x dx = ?
a) -e^(sin x) cos x + C
b) e^(sin x) + C
c) e^(sin x) sin x + C
d) -e^(sin x) + C
Answer: b) e^(sin x) + C
59. ∫ ln(x^2 + a^2) dx = ? (where a is a constant)
a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
b) 2x ln(x^2 + a^2) - 2x + C
c) x ln(x^2 + a^2) - x + a arctan(x/a) + C
d) (x^2 + a^2) ln(x^2 + a^2) - x^2 + C
Answer: a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
60. ∫ e^(ax^2) x dx = ? (where a is a constant, a ≠ 0)
a) 1/(2a) e^(ax^2) + C
b) x e^(ax^2) + C
c) e^(ax^2/2) + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/(2a) e^(ax^2) + C
61. ∫ ln(tan(x/2)) dx = ?
a) 2 ln|sec(x/2)| + C
b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
c) 2 ln|sin(x/2)| + C
d) tan(x/2) ln(tan(x/2)) + C
Answer: b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
62. ∫ e^(1/sin x) csc^2 x dx = ?
a) -e^(1/sin x) cot x + C
b) e^(1/sin x) + C
c) -e^(1/sin x) + C
d) e^(1/sin x) csc x + C
Answer: c) -e^(1/sin x) + C
63. ∫ ln(x + √(x^2 - 1)) dx = ?
a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
b) √(x^2 - 1) + C
c) x ln(x + √(x^2 - 1)) + C
d) ln(x + √(x^2 - 1)) + x + C
Answer: a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
64. ∫ e^(arcsin x) / √(1 - x^2) dx = ?
a) e^(arcsin x) + C
b) arcsin(x) e^(arcsin x) + C
c) x e^(arcsin x) + C
d) √(1 - x^2) e^(arcsin x) + C
Answer: a) e^(arcsin x) + C
65. ∫ ln(1 - x^2) dx = ?
a) x ln(1 - x^2) + 2x + C
b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
c) (1 - x^2) ln(1 - x^2) + x^2 + C
d) x ln(1 - x^2) - 2x + C
Answer: b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
66. ∫ e^(cos x) sin x dx = ?
a) -e^(cos x) + C
b) e^(cos x) + C
c) e^(cos x) sin x + C
d) -e^(cos x) cos x + C
Answer: a) -e^(cos x) + C
67. ∫ ln(x) √(1 - x^2) dx = ?
a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
b) x ln(x) √(1 - x^2) + C
c) ln(x) arcsin(x) + C
d) √(1 - x^2) ln(x) - x + C
Answer: a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
68. ∫ e^(x^3) x^2 dx = ?
a) 1/3 e^(x^3) + C
b) x e^(x^3) + C
c) e^(x^3) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/3 e^(x^3) + C
69. ∫ ln(sec x + tan x) sec x dx = ?
a) ln|sec x + tan x| + C
b) tan x ln(sec x + tan x) + C
c) sec x ln(sec x + tan x) + C
d) ln(sec x + tan x) + tan x + C
Answer: c) sec x ln(sec x + tan x) + C
70. ∫ e^(1/x) / x dx = ?
a) e^(1/x) + C
b) ln|x| e^(1/x) + C
c) Cannot be expressed in terms of elementary functions
d) -Ei(-1/x) + C
Answer: c) Cannot be expressed in terms of elementary functions
71. ∫ ln(x) / (1 - x^2) dx = ?
a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
b) ln(x) / √(1 - x^2) + C
c) arcsin(x) ln(x) + C
d) x ln(x) / (1 - x^2) + C
Answer: a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
52. ∫ e^(ax) cos(bx) dx = ? (where a and b are constants, a^2 + b^2 ≠ 0)
a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
b) e^(ax) (a cos(bx) - b sin(bx)) / (a^2 + b^2) + C
c) e^(ax) cos(bx) / (a + b) + C
d) e^(ax) (b cos(bx) - a sin(bx)) / (a^2 + b^2) + C
Answer: a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
53. ∫ ln(sec x + tan x) dx = ?
a) x ln(sec x + tan x) - x + C
b) ln|sec x + tan x| + C
c) sec x ln(sec x + tan x) + C
d) tan x + C
Answer: b) ln|sec x + tan x| + C
54. ∫ e^(x^2) erf(x) dx = ?
a) 1/2 e^(x^2) erf(x) + C
b) erf(x) / 2 + C
c) Cannot be expressed in terms of elementary functions
d) e^(x^2) + C
Answer: a) 1/2 e^(x^2) erf(x) + C
55. ∫ ln(x) / (x^2 + 1) dx = ?
a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
b) ln(x^2 + 1) / 2 - arctan(x) + C
c) x ln(x) / (x^2 + 1) + C
d) ln(x) arctan(x) + C
Answer: a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
56. ∫ e^(x^2) x^2 dx = ?
a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
b) 1/2 e^(x^2) + C
c) x^3 e^(x^2) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
57. ∫ ln(cosh x) dx = ?
a) x ln(cosh x) - sinh x + C
b) sinh x ln(cosh x) + C
c) x ln(cosh x) - x + C
d) cosh x ln(cosh x) - sinh x + C
Answer: a) x ln(cosh x) - sinh x + C
58. ∫ e^(sin x) sin x dx = ?
a) -e^(sin x) cos x + C
b) e^(sin x) + C
c) e^(sin x) sin x + C
d) -e^(sin x) + C
Answer: b) e^(sin x) + C
59. ∫ ln(x^2 + a^2) dx = ? (where a is a constant)
a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
b) 2x ln(x^2 + a^2) - 2x + C
c) x ln(x^2 + a^2) - x + a arctan(x/a) + C
d) (x^2 + a^2) ln(x^2 + a^2) - x^2 + C
Answer: a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
60. ∫ e^(ax^2) x dx = ? (where a is a constant, a ≠ 0)
a) 1/(2a) e^(ax^2) + C
b) x e^(ax^2) + C
c) e^(ax^2/2) + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/(2a) e^(ax^2) + C
61. ∫ ln(tan(x/2)) dx = ?
a) 2 ln|sec(x/2)| + C
b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
c) 2 ln|sin(x/2)| + C
d) tan(x/2) ln(tan(x/2)) + C
Answer: b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
62. ∫ e^(1/sin x) csc^2 x dx = ?
a) -e^(1/sin x) cot x + C
b) e^(1/sin x) + C
c) -e^(1/sin x) + C
d) e^(1/sin x) csc x + C
Answer: c) -e^(1/sin x) + C
63. ∫ ln(x + √(x^2 - 1)) dx = ?
a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
b) √(x^2 - 1) + C
c) x ln(x + √(x^2 - 1)) + C
d) ln(x + √(x^2 - 1)) + x + C
Answer: a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
64. ∫ e^(arcsin x) / √(1 - x^2) dx = ?
a) e^(arcsin x) + C
b) arcsin(x) e^(arcsin x) + C
c) x e^(arcsin x) + C
d) √(1 - x^2) e^(arcsin x) + C
Answer: a) e^(arcsin x) + C
65. ∫ ln(1 - x^2) dx = ?
a) x ln(1 - x^2) + 2x + C
b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
c) (1 - x^2) ln(1 - x^2) + x^2 + C
d) x ln(1 - x^2) - 2x + C
Answer: b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
66. ∫ e^(cos x) sin x dx = ?
a) -e^(cos x) + C
b) e^(cos x) + C
c) e^(cos x) sin x + C
d) -e^(cos x) cos x + C
Answer: a) -e^(cos x) + C
67. ∫ ln(x) √(1 - x^2) dx = ?
a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
b) x ln(x) √(1 - x^2) + C
c) ln(x) arcsin(x) + C
d) √(1 - x^2) ln(x) - x + C
Answer: a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
68. ∫ e^(x^3) x^2 dx = ?
a) 1/3 e^(x^3) + C
b) x e^(x^3) + C
c) e^(x^3) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/3 e^(x^3) + C
69. ∫ ln(sec x + tan x) sec x dx = ?
a) ln|sec x + tan x| + C
b) tan x ln(sec x + tan x) + C
c) sec x ln(sec x + tan x) + C
d) ln(sec x + tan x) + tan x + C
Answer: c) sec x ln(sec x + tan x) + C
70. ∫ e^(1/x) / x dx = ?
a) e^(1/x) + C
b) ln|x| e^(1/x) + C
c) Cannot be expressed in terms of elementary functions
d) -Ei(-1/x) + C
Answer: c) Cannot be expressed in terms of elementary functions
71. ∫ ln(x) / (1 - x^2) dx = ?
a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
b) ln(x) / √(1 - x^2) + C
c) arcsin(x) ln(x) + C
d) x ln(x) / (1 - x^2) + C
Answer: a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
52. ∫ e^(ax) cos(bx) dx = ? (where a and b are constants, a^2 + b^2 ≠ 0)
a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
b) e^(ax) (a cos(bx) - b sin(bx)) / (a^2 + b^2) + C
c) e^(ax) cos(bx) / (a + b) + C
d) e^(ax) (b cos(bx) - a sin(bx)) / (a^2 + b^2) + C
Answer: a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
53. ∫ ln(sec x + tan x) dx = ?
a) x ln(sec x + tan x) - x + C
b) ln|sec x + tan x| + C
c) sec x ln(sec x + tan x) + C
d) tan x + C
Answer: b) ln|sec x + tan x| + C
54. ∫ e^(x^2) erf(x) dx = ?
a) 1/2 e^(x^2) erf(x) + C
b) erf(x) / 2 + C
c) Cannot be expressed in terms of elementary functions
d) e^(x^2) + C
Answer: a) 1/2 e^(x^2) erf(x) + C
55. ∫ ln(x) / (x^2 + 1) dx = ?
a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
b) ln(x^2 + 1) / 2 - arctan(x) + C
c) x ln(x) / (x^2 + 1) + C
d) ln(x) arctan(x) + C
Answer: a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
56. ∫ e^(x^2) x^2 dx = ?
a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
b) 1/2 e^(x^2) + C
c) x^3 e^(x^2) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
57. ∫ ln(cosh x) dx = ?
a) x ln(cosh x) - sinh x + C
b) sinh x ln(cosh x) + C
c) x ln(cosh x) - x + C
d) cosh x ln(cosh x) - sinh x + C
Answer: a) x ln(cosh x) - sinh x + C
58. ∫ e^(sin x) sin x dx = ?
a) -e^(sin x) cos x + C
b) e^(sin x) + C
c) e^(sin x) sin x + C
d) -e^(sin x) + C
Answer: b) e^(sin x) + C
59. ∫ ln(x^2 + a^2) dx = ? (where a is a constant)
a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
b) 2x ln(x^2 + a^2) - 2x + C
c) x ln(x^2 + a^2) - x + a arctan(x/a) + C
d) (x^2 + a^2) ln(x^2 + a^2) - x^2 + C
Answer: a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
60. ∫ e^(ax^2) x dx = ? (where a is a constant, a ≠ 0)
a) 1/(2a) e^(ax^2) + C
b) x e^(ax^2) + C
c) e^(ax^2/2) + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/(2a) e^(ax^2) + C
61. ∫ ln(tan(x/2)) dx = ?
a) 2 ln|sec(x/2)| + C
b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
c) 2 ln|sin(x/2)| + C
d) tan(x/2) ln(tan(x/2)) + C
Answer: b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
62. ∫ e^(1/sin x) csc^2 x dx = ?
a) -e^(1/sin x) cot x + C
b) e^(1/sin x) + C
c) -e^(1/sin x) + C
d) e^(1/sin x) csc x + C
Answer: c) -e^(1/sin x) + C
63. ∫ ln(x + √(x^2 - 1)) dx = ?
a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
b) √(x^2 - 1) + C
c) x ln(x + √(x^2 - 1)) + C
d) ln(x + √(x^2 - 1)) + x + C
Answer: a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
64. ∫ e^(arcsin x) / √(1 - x^2) dx = ?
a) e^(arcsin x) + C
b) arcsin(x) e^(arcsin x) + C
c) x e^(arcsin x) + C
d) √(1 - x^2) e^(arcsin x) + C
Answer: a) e^(arcsin x) + C
65. ∫ ln(1 - x^2) dx = ?
a) x ln(1 - x^2) + 2x + C
b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
c) (1 - x^2) ln(1 - x^2) + x^2 + C
d) x ln(1 - x^2) - 2x + C
Answer: b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
66. ∫ e^(cos x) sin x dx = ?
a) -e^(cos x) + C
b) e^(cos x) + C
c) e^(cos x) sin x + C
d) -e^(cos x) cos x + C
Answer: a) -e^(cos x) + C
67. ∫ ln(x) √(1 - x^2) dx = ?
a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
b) x ln(x) √(1 - x^2) + C
c) ln(x) arcsin(x) + C
d) √(1 - x^2) ln(x) - x + C
Answer: a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
68. ∫ e^(x^3) x^2 dx = ?
a) 1/3 e^(x^3) + C
b) x e^(x^3) + C
c) e^(x^3) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/3 e^(x^3) + C
69. ∫ ln(sec x + tan x) sec x dx = ?
a) ln|sec x + tan x| + C
b) tan x ln(sec x + tan x) + C
c) sec x ln(sec x + tan x) + C
d) ln(sec x + tan x) + tan x + C
Answer: c) sec x ln(sec x + tan x) + C
70. ∫ e^(1/x) / x dx = ?
a) e^(1/x) + C
b) ln|x| e^(1/x) + C
c) Cannot be expressed in terms of elementary functions
d) -Ei(-1/x) + C
Answer: c) Cannot be expressed in terms of elementary functions
71. ∫ ln(x) / (1 - x^2) dx = ?
a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
b) ln(x) / √(1 - x^2) + C
c) arcsin(x) ln(x) + C
d) x ln(x) / (1 - x^2) + C
Answer: a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
52. ∫ e^(ax) cos(bx) dx = ? (where a and b are constants, a^2 + b^2 ≠ 0)
a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
b) e^(ax) (a cos(bx) - b sin(bx)) / (a^2 + b^2) + C
c) e^(ax) cos(bx) / (a + b) + C
d) e^(ax) (b cos(bx) - a sin(bx)) / (a^2 + b^2) + C
Answer: a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
53. ∫ ln(sec x + tan x) dx = ?
a) x ln(sec x + tan x) - x + C
b) ln|sec x + tan x| + C
c) sec x ln(sec x + tan x) + C
d) tan x + C
Answer: b) ln|sec x + tan x| + C
54. ∫ e^(x^2) erf(x) dx = ?
a) 1/2 e^(x^2) erf(x) + C
b) erf(x) / 2 + C
c) Cannot be expressed in terms of elementary functions
d) e^(x^2) + C
Answer: a) 1/2 e^(x^2) erf(x) + C
55. ∫ ln(x) / (x^2 + 1) dx = ?
a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
b) ln(x^2 + 1) / 2 - arctan(x) + C
c) x ln(x) / (x^2 + 1) + C
d) ln(x) arctan(x) + C
Answer: a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
56. ∫ e^(x^2) x^2 dx = ?
a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
b) 1/2 e^(x^2) + C
c) x^3 e^(x^2) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
57. ∫ ln(cosh x) dx = ?
a) x ln(cosh x) - sinh x + C
b) sinh x ln(cosh x) + C
c) x ln(cosh x) - x + C
d) cosh x ln(cosh x) - sinh x + C
Answer: a) x ln(cosh x) - sinh x + C
58. ∫ e^(sin x) sin x dx = ?
a) -e^(sin x) cos x + C
b) e^(sin x) + C
c) e^(sin x) sin x + C
d) -e^(sin x) + C
Answer: b) e^(sin x) + C
59. ∫ ln(x^2 + a^2) dx = ? (where a is a constant)
a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
b) 2x ln(x^2 + a^2) - 2x + C
c) x ln(x^2 + a^2) - x + a arctan(x/a) + C
d) (x^2 + a^2) ln(x^2 + a^2) - x^2 + C
Answer: a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
60. ∫ e^(ax^2) x dx = ? (where a is a constant, a ≠ 0)
a) 1/(2a) e^(ax^2) + C
b) x e^(ax^2) + C
c) e^(ax^2/2) + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/(2a) e^(ax^2) + C
61. ∫ ln(tan(x/2)) dx = ?
a) 2 ln|sec(x/2)| + C
b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
c) 2 ln|sin(x/2)| + C
d) tan(x/2) ln(tan(x/2)) + C
Answer: b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
62. ∫ e^(1/sin x) csc^2 x dx = ?
a) -e^(1/sin x) cot x + C
b) e^(1/sin x) + C
c) -e^(1/sin x) + C
d) e^(1/sin x) csc x + C
Answer: c) -e^(1/sin x) + C
63. ∫ ln(x + √(x^2 - 1)) dx = ?
a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
b) √(x^2 - 1) + C
c) x ln(x + √(x^2 - 1)) + C
d) ln(x + √(x^2 - 1)) + x + C
Answer: a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
64. ∫ e^(arcsin x) / √(1 - x^2) dx = ?
a) e^(arcsin x) + C
b) arcsin(x) e^(arcsin x) + C
c) x e^(arcsin x) + C
d) √(1 - x^2) e^(arcsin x) + C
Answer: a) e^(arcsin x) + C
65. ∫ ln(1 - x^2) dx = ?
a) x ln(1 - x^2) + 2x + C
b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
c) (1 - x^2) ln(1 - x^2) + x^2 + C
d) x ln(1 - x^2) - 2x + C
Answer: b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
66. ∫ e^(cos x) sin x dx = ?
a) -e^(cos x) + C
b) e^(cos x) + C
c) e^(cos x) sin x + C
d) -e^(cos x) cos x + C
Answer: a) -e^(cos x) + C
67. ∫ ln(x) √(1 - x^2) dx = ?
a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
b) x ln(x) √(1 - x^2) + C
c) ln(x) arcsin(x) + C
d) √(1 - x^2) ln(x) - x + C
Answer: a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
68. ∫ e^(x^3) x^2 dx = ?
a) 1/3 e^(x^3) + C
b) x e^(x^3) + C
c) e^(x^3) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/3 e^(x^3) + C
69. ∫ ln(sec x + tan x) sec x dx = ?
a) ln|sec x + tan x| + C
b) tan x ln(sec x + tan x) + C
c) sec x ln(sec x + tan x) + C
d) ln(sec x + tan x) + tan x + C
Answer: c) sec x ln(sec x + tan x) + C
70. ∫ e^(1/x) / x dx = ?
a) e^(1/x) + C
b) ln|x| e^(1/x) + C
c) Cannot be expressed in terms of elementary functions
d) -Ei(-1/x) + C
Answer: c) Cannot be expressed in terms of elementary functions
71. ∫ ln(x) / (1 - x^2) dx = ?
a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
b) ln(x) / √(1 - x^2) + C
c) arcsin(x) ln(x) + C
d) x ln(x) / (1 - x^2) + C
Answer: a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
52. ∫ e^(ax) cos(bx) dx = ? (where a and b are constants, a^2 + b^2 ≠ 0)
a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
b) e^(ax) (a cos(bx) - b sin(bx)) / (a^2 + b^2) + C
c) e^(ax) cos(bx) / (a + b) + C
d) e^(ax) (b cos(bx) - a sin(bx)) / (a^2 + b^2) + C
Answer: a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
53. ∫ ln(sec x + tan x) dx = ?
a) x ln(sec x + tan x) - x + C
b) ln|sec x + tan x| + C
c) sec x ln(sec x + tan x) + C
d) tan x + C
Answer: b) ln|sec x + tan x| + C
54. ∫ e^(x^2) erf(x) dx = ?
a) 1/2 e^(x^2) erf(x) + C
b) erf(x) / 2 + C
c) Cannot be expressed in terms of elementary functions
d) e^(x^2) + C
Answer: a) 1/2 e^(x^2) erf(x) + C
55. ∫ ln(x) / (x^2 + 1) dx = ?
a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
b) ln(x^2 + 1) / 2 - arctan(x) + C
c) x ln(x) / (x^2 + 1) + C
d) ln(x) arctan(x) + C
Answer: a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
56. ∫ e^(x^2) x^2 dx = ?
a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
b) 1/2 e^(x^2) + C
c) x^3 e^(x^2) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
57. ∫ ln(cosh x) dx = ?
a) x ln(cosh x) - sinh x + C
b) sinh x ln(cosh x) + C
c) x ln(cosh x) - x + C
d) cosh x ln(cosh x) - sinh x + C
Answer: a) x ln(cosh x) - sinh x + C
58. ∫ e^(sin x) sin x dx = ?
a) -e^(sin x) cos x + C
b) e^(sin x) + C
c) e^(sin x) sin x + C
d) -e^(sin x) + C
Answer: b) e^(sin x) + C
59. ∫ ln(x^2 + a^2) dx = ? (where a is a constant)
a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
b) 2x ln(x^2 + a^2) - 2x + C
c) x ln(x^2 + a^2) - x + a arctan(x/a) + C
d) (x^2 + a^2) ln(x^2 + a^2) - x^2 + C
Answer: a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
60. ∫ e^(ax^2) x dx = ? (where a is a constant, a ≠ 0)
a) 1/(2a) e^(ax^2) + C
b) x e^(ax^2) + C
c) e^(ax^2/2) + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/(2a) e^(ax^2) + C
61. ∫ ln(tan(x/2)) dx = ?
a) 2 ln|sec(x/2)| + C
b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
c) 2 ln|sin(x/2)| + C
d) tan(x/2) ln(tan(x/2)) + C
Answer: b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
62. ∫ e^(1/sin x) csc^2 x dx = ?
a) -e^(1/sin x) cot x + C
b) e^(1/sin x) + C
c) -e^(1/sin x) + C
d) e^(1/sin x) csc x + C
Answer: c) -e^(1/sin x) + C
63. ∫ ln(x + √(x^2 - 1)) dx = ?
a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
b) √(x^2 - 1) + C
c) x ln(x + √(x^2 - 1)) + C
d) ln(x + √(x^2 - 1)) + x + C
Answer: a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
64. ∫ e^(arcsin x) / √(1 - x^2) dx = ?
a) e^(arcsin x) + C
b) arcsin(x) e^(arcsin x) + C
c) x e^(arcsin x) + C
d) √(1 - x^2) e^(arcsin x) + C
Answer: a) e^(arcsin x) + C
65. ∫ ln(1 - x^2) dx = ?
a) x ln(1 - x^2) + 2x + C
b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
c) (1 - x^2) ln(1 - x^2) + x^2 + C
d) x ln(1 - x^2) - 2x + C
Answer: b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
66. ∫ e^(cos x) sin x dx = ?
a) -e^(cos x) + C
b) e^(cos x) + C
c) e^(cos x) sin x + C
d) -e^(cos x) cos x + C
Answer: a) -e^(cos x) + C
67. ∫ ln(x) √(1 - x^2) dx = ?
a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
b) x ln(x) √(1 - x^2) + C
c) ln(x) arcsin(x) + C
d) √(1 - x^2) ln(x) - x + C
Answer: a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
68. ∫ e^(x^3) x^2 dx = ?
a) 1/3 e^(x^3) + C
b) x e^(x^3) + C
c) e^(x^3) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/3 e^(x^3) + C
69. ∫ ln(sec x + tan x) sec x dx = ?
a) ln|sec x + tan x| + C
b) tan x ln(sec x + tan x) + C
c) sec x ln(sec x + tan x) + C
d) ln(sec x + tan x) + tan x + C
Answer: c) sec x ln(sec x + tan x) + C
70. ∫ e^(1/x) / x dx = ?
a) e^(1/x) + C
b) ln|x| e^(1/x) + C
c) Cannot be expressed in terms of elementary functions
d) -Ei(-1/x) + C
Answer: c) Cannot be expressed in terms of elementary functions
71. ∫ ln(x) / (1 - x^2) dx = ?
a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
b) ln(x) / √(1 - x^2) + C
c) arcsin(x) ln(x) + C
d) x ln(x) / (1 - x^2) + C
Answer: a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
52. ∫ e^(ax) cos(bx) dx = ? (where a and b are constants, a^2 + b^2 ≠ 0)
a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
b) e^(ax) (a cos(bx) - b sin(bx)) / (a^2 + b^2) + C
c) e^(ax) cos(bx) / (a + b) + C
d) e^(ax) (b cos(bx) - a sin(bx)) / (a^2 + b^2) + C
Answer: a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
53. ∫ ln(sec x + tan x) dx = ?
a) x ln(sec x + tan x) - x + C
b) ln|sec x + tan x| + C
c) sec x ln(sec x + tan x) + C
d) tan x + C
Answer: b) ln|sec x + tan x| + C
54. ∫ e^(x^2) erf(x) dx = ?
a) 1/2 e^(x^2) erf(x) + C
b) erf(x) / 2 + C
c) Cannot be expressed in terms of elementary functions
d) e^(x^2) + C
Answer: a) 1/2 e^(x^2) erf(x) + C
55. ∫ ln(x) / (x^2 + 1) dx = ?
a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
b) ln(x^2 + 1) / 2 - arctan(x) + C
c) x ln(x) / (x^2 + 1) + C
d) ln(x) arctan(x) + C
Answer: a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
56. ∫ e^(x^2) x^2 dx = ?
a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
b) 1/2 e^(x^2) + C
c) x^3 e^(x^2) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
57. ∫ ln(cosh x) dx = ?
a) x ln(cosh x) - sinh x + C
b) sinh x ln(cosh x) + C
c) x ln(cosh x) - x + C
d) cosh x ln(cosh x) - sinh x + C
Answer: a) x ln(cosh x) - sinh x + C
58. ∫ e^(sin x) sin x dx = ?
a) -e^(sin x) cos x + C
b) e^(sin x) + C
c) e^(sin x) sin x + C
d) -e^(sin x) + C
Answer: b) e^(sin x) + C
59. ∫ ln(x^2 + a^2) dx = ? (where a is a constant)
a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
b) 2x ln(x^2 + a^2) - 2x + C
c) x ln(x^2 + a^2) - x + a arctan(x/a) + C
d) (x^2 + a^2) ln(x^2 + a^2) - x^2 + C
Answer: a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
60. ∫ e^(ax^2) x dx = ? (where a is a constant, a ≠ 0)
a) 1/(2a) e^(ax^2) + C
b) x e^(ax^2) + C
c) e^(ax^2/2) + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/(2a) e^(ax^2) + C
61. ∫ ln(tan(x/2)) dx = ?
a) 2 ln|sec(x/2)| + C
b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
c) 2 ln|sin(x/2)| + C
d) tan(x/2) ln(tan(x/2)) + C
Answer: b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
62. ∫ e^(1/sin x) csc^2 x dx = ?
a) -e^(1/sin x) cot x + C
b) e^(1/sin x) + C
c) -e^(1/sin x) + C
d) e^(1/sin x) csc x + C
Answer: c) -e^(1/sin x) + C
63. ∫ ln(x + √(x^2 - 1)) dx = ?
a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
b) √(x^2 - 1) + C
c) x ln(x + √(x^2 - 1)) + C
d) ln(x + √(x^2 - 1)) + x + C
Answer: a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
64. ∫ e^(arcsin x) / √(1 - x^2) dx = ?
a) e^(arcsin x) + C
b) arcsin(x) e^(arcsin x) + C
c) x e^(arcsin x) + C
d) √(1 - x^2) e^(arcsin x) + C
Answer: a) e^(arcsin x) + C
65. ∫ ln(1 - x^2) dx = ?
a) x ln(1 - x^2) + 2x + C
b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
c) (1 - x^2) ln(1 - x^2) + x^2 + C
d) x ln(1 - x^2) - 2x + C
Answer: b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
66. ∫ e^(cos x) sin x dx = ?
a) -e^(cos x) + C
b) e^(cos x) + C
c) e^(cos x) sin x + C
d) -e^(cos x) cos x + C
Answer: a) -e^(cos x) + C
67. ∫ ln(x) √(1 - x^2) dx = ?
a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
b) x ln(x) √(1 - x^2) + C
c) ln(x) arcsin(x) + C
d) √(1 - x^2) ln(x) - x + C
Answer: a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
68. ∫ e^(x^3) x^2 dx = ?
a) 1/3 e^(x^3) + C
b) x e^(x^3) + C
c) e^(x^3) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/3 e^(x^3) + C
69. ∫ ln(sec x + tan x) sec x dx = ?
a) ln|sec x + tan x| + C
b) tan x ln(sec x + tan x) + C
c) sec x ln(sec x + tan x) + C
d) ln(sec x + tan x) + tan x + C
Answer: c) sec x ln(sec x + tan x) + C
70. ∫ e^(1/x) / x dx = ?
a) e^(1/x) + C
b) ln|x| e^(1/x) + C
c) Cannot be expressed in terms of elementary functions
d) -Ei(-1/x) + C
Answer: c) Cannot be expressed in terms of elementary functions
71. ∫ ln(x) / (1 - x^2) dx = ?
a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
b) ln(x) / √(1 - x^2) + C
c) arcsin(x) ln(x) + C
d) x ln(x) / (1 - x^2) + C
Answer: a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
52. ∫ e^(ax) cos(bx) dx = ? (where a and b are constants, a^2 + b^2 ≠ 0)
a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
b) e^(ax) (a cos(bx) - b sin(bx)) / (a^2 + b^2) + C
c) e^(ax) cos(bx) / (a + b) + C
d) e^(ax) (b cos(bx) - a sin(bx)) / (a^2 + b^2) + C
Answer: a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
53. ∫ ln(sec x + tan x) dx = ?
a) x ln(sec x + tan x) - x + C
b) ln|sec x + tan x| + C
c) sec x ln(sec x + tan x) + C
d) tan x + C
Answer: b) ln|sec x + tan x| + C
54. ∫ e^(x^2) erf(x) dx = ?
a) 1/2 e^(x^2) erf(x) + C
b) erf(x) / 2 + C
c) Cannot be expressed in terms of elementary functions
d) e^(x^2) + C
Answer: a) 1/2 e^(x^2) erf(x) + C
55. ∫ ln(x) / (x^2 + 1) dx = ?
a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
b) ln(x^2 + 1) / 2 - arctan(x) + C
c) x ln(x) / (x^2 + 1) + C
d) ln(x) arctan(x) + C
Answer: a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
56. ∫ e^(x^2) x^2 dx = ?
a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
b) 1/2 e^(x^2) + C
c) x^3 e^(x^2) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
57. ∫ ln(cosh x) dx = ?
a) x ln(cosh x) - sinh x + C
b) sinh x ln(cosh x) + C
c) x ln(cosh x) - x + C
d) cosh x ln(cosh x) - sinh x + C
Answer: a) x ln(cosh x) - sinh x + C
58. ∫ e^(sin x) sin x dx = ?
a) -e^(sin x) cos x + C
b) e^(sin x) + C
c) e^(sin x) sin x + C
d) -e^(sin x) + C
Answer: b) e^(sin x) + C
59. ∫ ln(x^2 + a^2) dx = ? (where a is a constant)
a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
b) 2x ln(x^2 + a^2) - 2x + C
c) x ln(x^2 + a^2) - x + a arctan(x/a) + C
d) (x^2 + a^2) ln(x^2 + a^2) - x^2 + C
Answer: a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
60. ∫ e^(ax^2) x dx = ? (where a is a constant, a ≠ 0)
a) 1/(2a) e^(ax^2) + C
b) x e^(ax^2) + C
c) e^(ax^2/2) + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/(2a) e^(ax^2) + C
61. ∫ ln(tan(x/2)) dx = ?
a) 2 ln|sec(x/2)| + C
b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
c) 2 ln|sin(x/2)| + C
d) tan(x/2) ln(tan(x/2)) + C
Answer: b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
62. ∫ e^(1/sin x) csc^2 x dx = ?
a) -e^(1/sin x) cot x + C
b) e^(1/sin x) + C
c) -e^(1/sin x) + C
d) e^(1/sin x) csc x + C
Answer: c) -e^(1/sin x) + C
63. ∫ ln(x + √(x^2 - 1)) dx = ?
a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
b) √(x^2 - 1) + C
c) x ln(x + √(x^2 - 1)) + C
d) ln(x + √(x^2 - 1)) + x + C
Answer: a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
64. ∫ e^(arcsin x) / √(1 - x^2) dx = ?
a) e^(arcsin x) + C
b) arcsin(x) e^(arcsin x) + C
c) x e^(arcsin x) + C
d) √(1 - x^2) e^(arcsin x) + C
Answer: a) e^(arcsin x) + C
65. ∫ ln(1 - x^2) dx = ?
a) x ln(1 - x^2) + 2x + C
b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
c) (1 - x^2) ln(1 - x^2) + x^2 + C
d) x ln(1 - x^2) - 2x + C
Answer: b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
66. ∫ e^(cos x) sin x dx = ?
a) -e^(cos x) + C
b) e^(cos x) + C
c) e^(cos x) sin x + C
d) -e^(cos x) cos x + C
Answer: a) -e^(cos x) + C
67. ∫ ln(x) √(1 - x^2) dx = ?
a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
b) x ln(x) √(1 - x^2) + C
c) ln(x) arcsin(x) + C
d) √(1 - x^2) ln(x) - x + C
Answer: a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
68. ∫ e^(x^3) x^2 dx = ?
a) 1/3 e^(x^3) + C
b) x e^(x^3) + C
c) e^(x^3) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/3 e^(x^3) + C
69. ∫ ln(sec x + tan x) sec x dx = ?
a) ln|sec x + tan x| + C
b) tan x ln(sec x + tan x) + C
c) sec x ln(sec x + tan x) + C
d) ln(sec x + tan x) + tan x + C
Answer: c) sec x ln(sec x + tan x) + C
70. ∫ e^(1/x) / x dx = ?
a) e^(1/x) + C
b) ln|x| e^(1/x) + C
c) Cannot be expressed in terms of elementary functions
d) -Ei(-1/x) + C
Answer: c) Cannot be expressed in terms of elementary functions
71. ∫ ln(x) / (1 - x^2) dx = ?
a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
b) ln(x) / √(1 - x^2) + C
c) arcsin(x) ln(x) + C
d) x ln(x) / (1 - x^2) + C
Answer: a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
52. ∫ e^(ax) cos(bx) dx = ? (where a and b are constants, a^2 + b^2 ≠ 0)
a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
b) e^(ax) (a cos(bx) - b sin(bx)) / (a^2 + b^2) + C
c) e^(ax) cos(bx) / (a + b) + C
d) e^(ax) (b cos(bx) - a sin(bx)) / (a^2 + b^2) + C
Answer: a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
53. ∫ ln(sec x + tan x) dx = ?
a) x ln(sec x + tan x) - x + C
b) ln|sec x + tan x| + C
c) sec x ln(sec x + tan x) + C
d) tan x + C
Answer: b) ln|sec x + tan x| + C
54. ∫ e^(x^2) erf(x) dx = ?
a) 1/2 e^(x^2) erf(x) + C
b) erf(x) / 2 + C
c) Cannot be expressed in terms of elementary functions
d) e^(x^2) + C
Answer: a) 1/2 e^(x^2) erf(x) + C
55. ∫ ln(x) / (x^2 + 1) dx = ?
a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
b) ln(x^2 + 1) / 2 - arctan(x) + C
c) x ln(x) / (x^2 + 1) + C
d) ln(x) arctan(x) + C
Answer: a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
56. ∫ e^(x^2) x^2 dx = ?
a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
b) 1/2 e^(x^2) + C
c) x^3 e^(x^2) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
57. ∫ ln(cosh x) dx = ?
a) x ln(cosh x) - sinh x + C
b) sinh x ln(cosh x) + C
c) x ln(cosh x) - x + C
d) cosh x ln(cosh x) - sinh x + C
Answer: a) x ln(cosh x) - sinh x + C
58. ∫ e^(sin x) sin x dx = ?
a) -e^(sin x) cos x + C
b) e^(sin x) + C
c) e^(sin x) sin x + C
d) -e^(sin x) + C
Answer: b) e^(sin x) + C
59. ∫ ln(x^2 + a^2) dx = ? (where a is a constant)
a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
b) 2x ln(x^2 + a^2) - 2x + C
c) x ln(x^2 + a^2) - x + a arctan(x/a) + C
d) (x^2 + a^2) ln(x^2 + a^2) - x^2 + C
Answer: a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
60. ∫ e^(ax^2) x dx = ? (where a is a constant, a ≠ 0)
a) 1/(2a) e^(ax^2) + C
b) x e^(ax^2) + C
c) e^(ax^2/2) + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/(2a) e^(ax^2) + C
61. ∫ ln(tan(x/2)) dx = ?
a) 2 ln|sec(x/2)| + C
b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
c) 2 ln|sin(x/2)| + C
d) tan(x/2) ln(tan(x/2)) + C
Answer: b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
62. ∫ e^(1/sin x) csc^2 x dx = ?
a) -e^(1/sin x) cot x + C
b) e^(1/sin x) + C
c) -e^(1/sin x) + C
d) e^(1/sin x) csc x + C
Answer: c) -e^(1/sin x) + C
63. ∫ ln(x + √(x^2 - 1)) dx = ?
a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
b) √(x^2 - 1) + C
c) x ln(x + √(x^2 - 1)) + C
d) ln(x + √(x^2 - 1)) + x + C
Answer: a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
64. ∫ e^(arcsin x) / √(1 - x^2) dx = ?
a) e^(arcsin x) + C
b) arcsin(x) e^(arcsin x) + C
c) x e^(arcsin x) + C
d) √(1 - x^2) e^(arcsin x) + C
Answer: a) e^(arcsin x) + C
65. ∫ ln(1 - x^2) dx = ?
a) x ln(1 - x^2) + 2x + C
b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
c) (1 - x^2) ln(1 - x^2) + x^2 + C
d) x ln(1 - x^2) - 2x + C
Answer: b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
66. ∫ e^(cos x) sin x dx = ?
a) -e^(cos x) + C
b) e^(cos x) + C
c) e^(cos x) sin x + C
d) -e^(cos x) cos x + C
Answer: a) -e^(cos x) + C
67. ∫ ln(x) √(1 - x^2) dx = ?
a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
b) x ln(x) √(1 - x^2) + C
c) ln(x) arcsin(x) + C
d) √(1 - x^2) ln(x) - x + C
Answer: a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
68. ∫ e^(x^3) x^2 dx = ?
a) 1/3 e^(x^3) + C
b) x e^(x^3) + C
c) e^(x^3) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/3 e^(x^3) + C
69. ∫ ln(sec x + tan x) sec x dx = ?
a) ln|sec x + tan x| + C
b) tan x ln(sec x + tan x) + C
c) sec x ln(sec x + tan x) + C
d) ln(sec x + tan x) + tan x + C
Answer: c) sec x ln(sec x + tan x) + C
70. ∫ e^(1/x) / x dx = ?
a) e^(1/x) + C
b) ln|x| e^(1/x) + C
c) Cannot be expressed in terms of elementary functions
d) -Ei(-1/x) + C
Answer: c) Cannot be expressed in terms of elementary functions
71. ∫ ln(x) / (1 - x^2) dx = ?
a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
b) ln(x) / √(1 - x^2) + C
c) arcsin(x) ln(x) + C
d) x ln(x) / (1 - x^2) + C
Answer: a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
52. ∫ e^(ax) cos(bx) dx = ? (where a and b are constants, a^2 + b^2 ≠ 0)
a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
b) e^(ax) (a cos(bx) - b sin(bx)) / (a^2 + b^2) + C
c) e^(ax) cos(bx) / (a + b) + C
d) e^(ax) (b cos(bx) - a sin(bx)) / (a^2 + b^2) + C
Answer: a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
53. ∫ ln(sec x + tan x) dx = ?
a) x ln(sec x + tan x) - x + C
b) ln|sec x + tan x| + C
c) sec x ln(sec x + tan x) + C
d) tan x + C
Answer: b) ln|sec x + tan x| + C
54. ∫ e^(x^2) erf(x) dx = ?
a) 1/2 e^(x^2) erf(x) + C
b) erf(x) / 2 + C
c) Cannot be expressed in terms of elementary functions
d) e^(x^2) + C
Answer: a) 1/2 e^(x^2) erf(x) + C
55. ∫ ln(x) / (x^2 + 1) dx = ?
a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
b) ln(x^2 + 1) / 2 - arctan(x) + C
c) x ln(x) / (x^2 + 1) + C
d) ln(x) arctan(x) + C
Answer: a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
56. ∫ e^(x^2) x^2 dx = ?
a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
b) 1/2 e^(x^2) + C
c) x^3 e^(x^2) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
57. ∫ ln(cosh x) dx = ?
a) x ln(cosh x) - sinh x + C
b) sinh x ln(cosh x) + C
c) x ln(cosh x) - x + C
d) cosh x ln(cosh x) - sinh x + C
Answer: a) x ln(cosh x) - sinh x + C
58. ∫ e^(sin x) sin x dx = ?
a) -e^(sin x) cos x + C
b) e^(sin x) + C
c) e^(sin x) sin x + C
d) -e^(sin x) + C
Answer: b) e^(sin x) + C
59. ∫ ln(x^2 + a^2) dx = ? (where a is a constant)
a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
b) 2x ln(x^2 + a^2) - 2x + C
c) x ln(x^2 + a^2) - x + a arctan(x/a) + C
d) (x^2 + a^2) ln(x^2 + a^2) - x^2 + C
Answer: a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
60. ∫ e^(ax^2) x dx = ? (where a is a constant, a ≠ 0)
a) 1/(2a) e^(ax^2) + C
b) x e^(ax^2) + C
c) e^(ax^2/2) + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/(2a) e^(ax^2) + C
61. ∫ ln(tan(x/2)) dx = ?
a) 2 ln|sec(x/2)| + C
b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
c) 2 ln|sin(x/2)| + C
d) tan(x/2) ln(tan(x/2)) + C
Answer: b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
62. ∫ e^(1/sin x) csc^2 x dx = ?
a) -e^(1/sin x) cot x + C
b) e^(1/sin x) + C
c) -e^(1/sin x) + C
d) e^(1/sin x) csc x + C
Answer: c) -e^(1/sin x) + C
63. ∫ ln(x + √(x^2 - 1)) dx = ?
a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
b) √(x^2 - 1) + C
c) x ln(x + √(x^2 - 1)) + C
d) ln(x + √(x^2 - 1)) + x + C
Answer: a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
64. ∫ e^(arcsin x) / √(1 - x^2) dx = ?
a) e^(arcsin x) + C
b) arcsin(x) e^(arcsin x) + C
c) x e^(arcsin x) + C
d) √(1 - x^2) e^(arcsin x) + C
Answer: a) e^(arcsin x) + C
65. ∫ ln(1 - x^2) dx = ?
a) x ln(1 - x^2) + 2x + C
b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
c) (1 - x^2) ln(1 - x^2) + x^2 + C
d) x ln(1 - x^2) - 2x + C
Answer: b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
66. ∫ e^(cos x) sin x dx = ?
a) -e^(cos x) + C
b) e^(cos x) + C
c) e^(cos x) sin x + C
d) -e^(cos x) cos x + C
Answer: a) -e^(cos x) + C
67. ∫ ln(x) √(1 - x^2) dx = ?
a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
b) x ln(x) √(1 - x^2) + C
c) ln(x) arcsin(x) + C
d) √(1 - x^2) ln(x) - x + C
Answer: a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
68. ∫ e^(x^3) x^2 dx = ?
a) 1/3 e^(x^3) + C
b) x e^(x^3) + C
c) e^(x^3) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/3 e^(x^3) + C
69. ∫ ln(sec x + tan x) sec x dx = ?
a) ln|sec x + tan x| + C
b) tan x ln(sec x + tan x) + C
c) sec x ln(sec x + tan x) + C
d) ln(sec x + tan x) + tan x + C
Answer: c) sec x ln(sec x + tan x) + C
70. ∫ e^(1/x) / x dx = ?
a) e^(1/x) + C
b) ln|x| e^(1/x) + C
c) Cannot be expressed in terms of elementary functions
d) -Ei(-1/x) + C
Answer: c) Cannot be expressed in terms of elementary functions
71. ∫ ln(x) / (1 - x^2) dx = ?
a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
b) ln(x) / √(1 - x^2) + C
c) arcsin(x) ln(x) + C
d) x ln(x) / (1 - x^2) + C
Answer: a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
52. ∫ e^(ax) cos(bx) dx = ? (where a and b are constants, a^2 + b^2 ≠ 0)
a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
b) e^(ax) (a cos(bx) - b sin(bx)) / (a^2 + b^2) + C
c) e^(ax) cos(bx) / (a + b) + C
d) e^(ax) (b cos(bx) - a sin(bx)) / (a^2 + b^2) + C
Answer: a) e^(ax) (a cos(bx) + b sin(bx)) / (a^2 + b^2) + C
53. ∫ ln(sec x + tan x) dx = ?
a) x ln(sec x + tan x) - x + C
b) ln|sec x + tan x| + C
c) sec x ln(sec x + tan x) + C
d) tan x + C
Answer: b) ln|sec x + tan x| + C
54. ∫ e^(x^2) erf(x) dx = ?
a) 1/2 e^(x^2) erf(x) + C
b) erf(x) / 2 + C
c) Cannot be expressed in terms of elementary functions
d) e^(x^2) + C
Answer: a) 1/2 e^(x^2) erf(x) + C
55. ∫ ln(x) / (x^2 + 1) dx = ?
a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
b) ln(x^2 + 1) / 2 - arctan(x) + C
c) x ln(x) / (x^2 + 1) + C
d) ln(x) arctan(x) + C
Answer: a) arctan(x) ln(x) - ∫ arctan(x) / x dx + C
56. ∫ e^(x^2) x^2 dx = ?
a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
b) 1/2 e^(x^2) + C
c) x^3 e^(x^2) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/2 x e^(x^2) - 1/4 ∫ e^(x^2) dx + C
57. ∫ ln(cosh x) dx = ?
a) x ln(cosh x) - sinh x + C
b) sinh x ln(cosh x) + C
c) x ln(cosh x) - x + C
d) cosh x ln(cosh x) - sinh x + C
Answer: a) x ln(cosh x) - sinh x + C
58. ∫ e^(sin x) sin x dx = ?
a) -e^(sin x) cos x + C
b) e^(sin x) + C
c) e^(sin x) sin x + C
d) -e^(sin x) + C
Answer: b) e^(sin x) + C
59. ∫ ln(x^2 + a^2) dx = ? (where a is a constant)
a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
b) 2x ln(x^2 + a^2) - 2x + C
c) x ln(x^2 + a^2) - x + a arctan(x/a) + C
d) (x^2 + a^2) ln(x^2 + a^2) - x^2 + C
Answer: a) x ln(x^2 + a^2) - 2x + 2a arctan(x/a) + C
60. ∫ e^(ax^2) x dx = ? (where a is a constant, a ≠ 0)
a) 1/(2a) e^(ax^2) + C
b) x e^(ax^2) + C
c) e^(ax^2/2) + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/(2a) e^(ax^2) + C
61. ∫ ln(tan(x/2)) dx = ?
a) 2 ln|sec(x/2)| + C
b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
c) 2 ln|sin(x/2)| + C
d) tan(x/2) ln(tan(x/2)) + C
Answer: b) x ln(tan(x/2)) - 2 ln|cos(x/2)| + C
62. ∫ e^(1/sin x) csc^2 x dx = ?
a) -e^(1/sin x) cot x + C
b) e^(1/sin x) + C
c) -e^(1/sin x) + C
d) e^(1/sin x) csc x + C
Answer: c) -e^(1/sin x) + C
63. ∫ ln(x + √(x^2 - 1)) dx = ?
a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
b) √(x^2 - 1) + C
c) x ln(x + √(x^2 - 1)) + C
d) ln(x + √(x^2 - 1)) + x + C
Answer: a) x ln(x + √(x^2 - 1)) - √(x^2 - 1) + C
64. ∫ e^(arcsin x) / √(1 - x^2) dx = ?
a) e^(arcsin x) + C
b) arcsin(x) e^(arcsin x) + C
c) x e^(arcsin x) + C
d) √(1 - x^2) e^(arcsin x) + C
Answer: a) e^(arcsin x) + C
65. ∫ ln(1 - x^2) dx = ?
a) x ln(1 - x^2) + 2x + C
b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
c) (1 - x^2) ln(1 - x^2) + x^2 + C
d) x ln(1 - x^2) - 2x + C
Answer: b) x ln(1 - x^2) - 2x + 2 arctan(x) + C
66. ∫ e^(cos x) sin x dx = ?
a) -e^(cos x) + C
b) e^(cos x) + C
c) e^(cos x) sin x + C
d) -e^(cos x) cos x + C
Answer: a) -e^(cos x) + C
67. ∫ ln(x) √(1 - x^2) dx = ?
a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
b) x ln(x) √(1 - x^2) + C
c) ln(x) arcsin(x) + C
d) √(1 - x^2) ln(x) - x + C
Answer: a) 1/2 x √(1 - x^2) ln(x) - 1/4 x √(1 - x^2) - 1/4 arcsin(x) + C
68. ∫ e^(x^3) x^2 dx = ?
a) 1/3 e^(x^3) + C
b) x e^(x^3) + C
c) e^(x^3) / 3 + C
d) Cannot be expressed in terms of elementary functions
Answer: a) 1/3 e^(x^3) + C
69. ∫ ln(sec x + tan x) sec x dx = ?
a) ln|sec x + tan x| + C
b) tan x ln(sec x + tan x) + C
c) sec x ln(sec x + tan x) + C
d) ln(sec x + tan x) + tan x + C
Answer: c) sec x ln(sec x + tan x) + C
70. ∫ e^(1/x) / x dx = ?
a) e^(1/x) + C
b) ln|x| e^(1/x) + C
c) Cannot be expressed in terms of elementary functions
d) -Ei(-1/x) + C
Answer: c) Cannot be expressed in terms of elementary functions
71. ∫ ln(x) / (1 - x^2) dx = ?
a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
b) ln(x) / √(1 - x^2) + C
c) arcsin(x) ln(x) + C
d) x ln(x) / (1 - x^2) + C
Answer: a) 1/2 ln((1 + x) / (1 - x)) ln(x) + Li_2(x) - Li_2(-x) + C
72. ∫ e^(tan x) sec x dx = ?
a) e^(tan x) + C
b) tan(x) e^(tan x) + C
c) sec(x) e^(tan x) + C
Students also viewed