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MULTIPLE CHOICE QUESTIONS INTEGRATION OF TRIGONOMETRIC FUNCTIONS

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MULTIPLE CHOICE QUESTIONS: INTEGRATION OF TRIGONOMETRIC
FUNCTIONS
1. ∫ sin x dx
a) -cos x + C
b) cos x + C
c) tan x + C
d) sec x + C
Answer: a) -cos x + C
2. ∫ cos x dx
a) sin x + C
b) -sin x + C
c) tan x + C
d) sec x + C
Answer: a) sin x + C
3. ∫ tan x dx
a) sec x + C
b) csc x + C
c) -ln|cos x| + C
d) ln|sec x| + C
Answer: c) -ln|cos x| + C
4. ∫ cot x dx
a) tan x + C
b) sec x + C
c) ln|sin x| + C
d) -ln|sin x| + C
Answer: c) ln|sin x| + C
5. ∫ sec x dx
a) tan x + C
b) ln|sec x + tan x| + C
c) ln|csc x + cot x| + C
d) csc x + C
Answer: b) ln|sec x + tan x| + C
6. ∫ csc x dx
a) tan x + C
b) ln|sec x + tan x| + C
c) -ln|csc x + cot x| + C
d) sec x + C
Answer: c) -ln|csc x + cot x| + C
7. ∫ sin^2 x dx
a) x/2 - sin(2x)/4 + C
b) x/2 + sin(2x)/4 + C
c) -cos(2x)/4 + C
d) cos(2x)/4 + C
Answer: a) x/2 - sin(2x)/4 + C
8. ∫ cos^2 x dx
a) x/2 - sin(2x)/4 + C
b) x/2 + sin(2x)/4 + C
c) -cos(2x)/4 + C
d) cos(2x)/4 + C
Answer: b) x/2 + sin(2x)/4 + C
9. ∫ tan^2 x dx
a) tan x - x + C
b) -tan x + x + C
c) cot x - x + C
d) -cot x + x + C
Answer: a) tan x - x + C
10. ∫ cot^2 x dx
a) tan x - x + C
b) -tan x + x + C
c) cot x - x + C
d) -cot x + x + C
Answer: d) -cot x + x + C
11. ∫ sec^2 x dx
a) tan x + C
b) -tan x + C
c) cot x + C
d) -cot x + C
Answer: a) tan x + C
12. ∫ csc^2 x dx
a) tan x + C
b) -tan x + C
c) cot x + C
d) -cot x + C
Answer: d) -cot x + C
13. ∫ sin x cos x dx
a) sin^2 x/2 + C
b) -cos^2 x/2 + C
c) tan x + C
d) cot x + C
Answer: a) sin^2 x/2 + C
14. ∫ sin^3 x dx
a) -cos x + cos^3 x/3 + C
b) cos x - cos^3 x/3 + C
c) -cos x (1 - 2sin^2 x)/3 + C
d) cos x (1 - 2sin^2 x)/3 + C
Answer: a) -cos x + cos^3 x/3 + C
15. ∫ cos^3 x dx
a) sin x - sin^3 x/3 + C
b) -sin x + sin^3 x/3 + C
c) sin x (2 - sin^2 x)/3 + C
d) -sin x (2 - sin^2 x)/3 + C
Answer: c) sin x (2 - sin^2 x)/3 + C
16. ∫ tan^3 x dx
a) ln|cos x| - tan^2 x/2 + C
b) -ln|cos x| + tan^2 x/2 + C
c) ln|sec x| + tan^2 x/2 + C
d) -ln|sec x| - tan^2 x/2 + C
Answer: b) -ln|cos x| + tan^2 x/2 + C
17. ∫ cot^3 x dx
a) ln|sin x| - cot^2 x/2 + C
b) -ln|sin x| + cot^2 x/2 + C
c) ln|csc x| + cot^2 x/2 + C
d) -ln|csc x| - cot^2 x/2 + C
Answer: a) ln|sin x| - cot^2 x/2 + C
18. ∫ sec^3 x dx
a) tan x sec x/2 + ln|sec x + tan x| + C
b) tan x sec x/2 - ln|sec x + tan x| + C
c) -tan x sec x/2 + ln|sec x + tan x| + C
d) -tan x sec x/2 - ln|sec x + tan x| + C
Answer: a) tan x sec x/2 + ln|sec x + tan x| + C
19. ∫ csc^3 x dx
a) -cot x csc x/2 - ln|csc x + cot x| + C
b) -cot x csc x/2 + ln|csc x + cot x| + C
c) cot x csc x/2 - ln|csc x + cot x| + C
d) cot x csc x/2 + ln|csc x + cot x| + C
Answer: a) -cot x csc x/2 - ln|csc x + cot x| + C
20. ∫ sin^4 x dx
a) 3x/8 - sin(2x)/4 + sin(4x)/32 + C
b) 3x/8 + sin(2x)/4 - sin(4x)/32 + C
c) -3x/8 + sin(2x)/4 - sin(4x)/32 + C
d) -3x/8 - sin(2x)/4 + sin(4x)/32 + C
Answer: a) 3x/8 - sin(2x)/4 + sin(4x)/32 + C
21. ∫ cos^4 x dx
a) 3x/8 - sin(2x)/4 + sin(4x)/32 + C
b) 3x/8 + sin(2x)/4 - sin(4x)/32 + C
c) -3x/8 + sin(2x)/4 - sin(4x)/32 + C
d) -3x/8 - sin(2x)/4 + sin(4x)/32 + C
Answer: b) 3x/8 + sin(2x)/4 - sin(4x)/32 + C
22. ∫ sin x cos^2 x dx
a) sin^3 x/3 + C
b) -sin^3 x/3 + C
c) cos^3 x/3 + C
d) -cos^3 x/3 + C
Answer: a) sin^3 x/3 + C
23. ∫ sin^2 x cos x dx
a) -cos^3 x/3 + C
b) cos^3 x/3 + C
c) sin^3 x/3 + C
d) -sin^3 x/3 + C
Answer: a) -cos^3 x/3 + C
24. ∫ tan x sec^2 x dx
a) tan^2 x/2 + C
b) -tan^2 x/2 + C
c) sec^2 x/2 + C
d) -sec^2 x/2 + C
Answer: a) tan^2 x/2 + C
25. ∫ cot x csc^2 x dx
a) cot^2 x/2 + C
b) -cot^2 x/2 + C
c) csc^2 x/2 + C
d) -csc^2 x/2 + C
Answer: b) -cot^2 x/2 + C
26. ∫ sin(2x) dx
a) -cos(2x)/2 + C
b) cos(2x)/2 + C
c) sin(2x)/2 + C
d) -sin(2x)/2 + C
Answer: a) -cos(2x)/2 + C
27. ∫ cos(2x) dx
a) sin(2x)/2 + C
b) -sin(2x)/2 + C
c) cos(2x)/2 + C
d) -cos(2x)/2 + C
Answer: a) sin(2x)/2 + C
28. ∫ tan(2x) dx
a) -ln|cos(2x)|/2 + C
b) ln|cos(2x)|/2 + C
c) -ln|sec(2x)| + C
d) ln|sec(2x)| + C
Answer: a) -ln|cos(2x)|/2 + C
29. ∫ sec(2x) dx
a) ln|sec(2x) + tan(2x)|/2 + C
b) -ln|sec(2x) + tan(2x)|/2 + C
c) ln|csc(2x) + cot(2x)|/2 + C
d) -ln|csc(2x) + cot(2x)|/2 + C
Answer: a) ln|sec(2x) + tan(2x)|/2 + C
30. ∫ sin^2(2x) dx
a) x/2 - sin(4x)/8 + C
b) x/2 + sin(4x)/8 + C
c) -x/2 + sin(4x)/8 + C
d) -x/2 - sin(4x)/8 + C
Answer: a) x/2 - sin(4x)/8 + C
31. ∫ cos^2(2x) dx
a) x/2 - sin(4x)/8 + C
b) x/2 + sin(4x)/8 + C
c) -x/2 + sin(4x)/8 + C
d) -x/2 - sin(4x)/8 + C
Answer: b) x/2 + sin(4x)/8 + C
32. ∫ sin(3x) dx
a) -cos(3x)/3 + C
b) cos(3x)/3 + C
c) sin(3x)/3 + C
d) -sin(3x)/3 + C
Answer: a) -cos(3x)/3 + C
33. ∫ cos(3x) dx
a) sin(3x)/3 + C
b) -sin(3x)/3 + C
c) cos(3x)/3 + C
d) -cos(3x)/3 + C
Answer: a) sin(3x)/3 + C
34. ∫ tan(3x) dx
a) -ln|cos(3x)|/3 + C
b) ln|cos(3x)|/3 + C
c) -ln|sec(3x)| + C
d) ln|sec(3x)| + C
Answer: a) -ln|cos(3x)|/3 + C
35. ∫ sec(3x) dx
a) ln|sec(3x) + tan(3x)|/3 + C
b) -ln|sec(3x) + tan(3x)|/3 + C
c) ln|csc(3x) + cot(3x)|/3 + C
d) -ln|csc(3x) + cot(3x)|/3 + C
Answer: a) ln|sec(3x) + tan(3x)|/3 + C
36. ∫ sin x cos x dx
a) sin^2 x/2 + C
b) -sin^2 x/2 + C
c) cos^2 x/2 + C
d) -cos^2 x/2 + C
Answer: a) sin^2 x/2 + C
37. ∫ sin^2 x cos^2 x dx
a) x/8 - sin(4x)/32 + C
b) x/8 + sin(4x)/32 + C
c) -x/8 + sin(4x)/32 + C
d) -x/8 - sin(4x)/32 + C
Answer: a) x/8 - sin(4x)/32 + C
38. ∫ sin^3 x cos^2 x dx
a) cos^5 x/5 - cos^3 x/3 + C
b) -cos^5 x/5 + cos^3 x/3 + C
c) sin^5 x/5 - sin^3 x/3 + C
d) -sin^5 x/5 + sin^3 x/3 + C
Answer: b) -cos^5 x/5 + cos^3 x/3 + C
39. ∫ sin^2 x cos^3 x dx
a) sin^5 x/5 - sin^3 x/3 + C
b) -sin^5 x/5 + sin^3 x/3 + C
c) cos^5 x/5 - cos^3 x/3 + C
d) -cos^5 x/5 + cos^3 x/3 + C
Answer: a) sin^5 x/5 - sin^3 x/3 + C
40. ∫ tan x sec x dx
a) sec x + C
b) -sec x + C
c) tan x + C
d) -tan x + C
Answer: a) sec x + C
41. ∫ cot x csc x dx
a) csc x + C
b) -csc x + C
c) cot x + C
d) -cot x + C
Answer: b) -csc x + C
42. ∫ sin(x/2) dx
a) -2cos(x/2) + C
b) 2cos(x/2) + C
c) sin(x/2) + C
d) -sin(x/2) + C
Answer: a) -2cos(x/2) + C
43. ∫ cos(x/2) dx
a) 2sin(x/2) + C
b) -2sin(x/2) + C
c) cos(x/2) + C
d) -cos(x/2) + C
Answer: a) 2sin(x/2) + C
44. ∫ tan(x/2) dx
a) -2ln|cos(x/2)| + C
b) 2ln|cos(x/2)| + C
c) -2ln|sec(x/2)| + C
d) 2ln|sec(x/2)| + C
Answer: c) -2ln|sec(x/2)| + C
45. ∫ sec(x/2) dx
a) 2ln|sec(x/2) + tan(x/2)| + C
b) -2ln|sec(x/2) + tan(x/2)| + C
c) ln|sec(x/2) + tan(x/2)| + C
d) -ln|sec(x/2) + tan(x/2)| + C
Answer: a) 2ln|sec(x/2) + tan(x/2)| + C
46. ∫ sin^2(x/2) dx
a) x/2 - sin(x)/2 + C
b) x/2 + sin(x)/2 + C
c) -x/2 + sin(x)/2 + C
d) -x/2 - sin(x)/2 + C
Answer: a) x/2 - sin(x)/2 + C
47. ∫ cos^2(x/2) dx
a) x/2 - sin(x)/2 + C
b) x/2 + sin(x)/2 + C
c) -x/2 + sin(x)/2 + C
d) -x/2 - sin(x)/2 + C
Answer: b) x/2 + sin(x)/2 + C
48. ∫ sin x cos(2x) dx
a) -sin(3x)/6 + sin x/2 + C
b) sin(3x)/6 - sin x/2 + C
c) -sin(3x)/6 - sin x/2 + C
d) sin(3x)/6 + sin x/2 + C
Answer: a) -sin(3x)/6 + sin x/2 + C
49. ∫ sin(2x) cos x dx
a) -cos(3x)/6 - cos x/2 + C
b) cos(3x)/6 + cos x/2 + C
c) -cos(3x)/6 + cos x/2 + C
d) cos(3x)/6 - cos x/2 + C
Answer: b) cos(3x)/6 + cos x/2 + C
50. ∫ sin x sin(2x) dx
a) -cos(3x)/6 + cos x/2 + C
b) cos(3x)/6 - cos x/2 + C
c) -cos(3x)/6 - cos x/2 + C
d) cos(3x)/6 + cos x/2 + C
Answer: b) cos(3x)/6 - cos x/2 + C
51. ∫ cos x cos(2x) dx
a) sin(3x)/6 + sin x/2 + C
b) -sin(3x)/6 - sin x/2 + C
c) sin(3x)/6 - sin x/2 + C
d) -sin(3x)/6 + sin x/2 + C
Answer: c) sin(3x)/6 - sin x/2 + C
52. ∫ sin^2 x cos^2 x dx
a) x/8 - sin(4x)/32 + C
b) x/8 + sin(4x)/32 + C
c) -x/8 + sin(4x)/32 + C
d) -x/8 - sin(4x)/32 + C
Answer: a) x/8 - sin(4x)/32 + C
53. ∫ sin^2 x cos^4 x dx
a) x/16 - sin(2x)/32 - sin(4x)/96 - sin(6x)/480 + C
b) x/16 + sin(2x)/32 + sin(4x)/96 + sin(6x)/480 + C
c) -x/16 + sin(2x)/32 + sin(4x)/96 + sin(6x)/480 + C
d) -x/16 - sin(2x)/32 - sin(4x)/96 - sin(6x)/480 + C
Answer: a) x/16 - sin(2x)/32 - sin(4x)/96 - sin(6x)/480 + C
54. ∫ sin^4 x cos^2 x dx
a) x/16 - sin(2x)/32 + sin(4x)/96 - sin(6x)/480 + C
b) x/16 + sin(2x)/32 - sin(4x)/96 + sin(6x)/480 + C
c) -x/16 + sin(2x)/32 - sin(4x)/96 + sin(6x)/480 + C
d) -x/16 - sin(2x)/32 + sin(4x)/96 - sin(6x)/480 + C
Answer: a) x/16 - sin(2x)/32 + sin(4x)/96 - sin(6x)/480 + C
55. ∫ tan^4 x dx
a) tan^3 x/3 - tan x + x + C
b) -tan^3 x/3 + tan x - x + C
c) tan^3 x/3 + tan x - x + C
d) -tan^3 x/3 - tan x + x + C
Answer: c) tan^3 x/3 + tan x - x + C
56. ∫ cot^4 x dx
a) -cot^3 x/3 - cot x - x + C
b) cot^3 x/3 + cot x + x + C
c) -cot^3 x/3 + cot x - x + C
d) cot^3 x/3 - cot x + x + C
Answer: a) -cot^3 x/3 - cot x - x + C
57. ∫ sec^4 x dx
a) tan^3 x/3 + tan x + C
b) -tan^3 x/3 - tan x + C
c) tan^3 x/3 - tan x + C
d) -tan^3 x/3 + tan x + C
Answer: a) tan^3 x/3 + tan x + C
58. ∫ csc^4 x dx
a) -cot^3 x/3 - cot x + C
b) cot^3 x/3 + cot x + C
c) -cot^3 x/3 + cot x + C
d) cot^3 x/3 - cot x + C
Answer: a) -cot^3 x/3 - cot x + C
59. ∫ sin(3x) cos(2x) dx
a) -sin(5x)/10 + sin x/6 + C
b) sin(5x)/10 - sin x/6 + C
c) -sin(5x)/10 - sin x/6 + C
d) sin(5x)/10 + sin x/6 + C
Answer: b) sin(5x)/10 - sin x/6 + C
60. ∫ sin(2x) cos(3x) dx
a) -cos(5x)/10 - cos x/4 + C
b) cos(5x)/10 + cos x/4 + C
c) -cos(5x)/10 + cos x/4 + C
d) cos(5x)/10 - cos x/4 + C
Answer: b) cos(5x)/10 + cos x/4 + C
61. ∫ sin^2(2x) cos(2x) dx
a) -sin^3(2x)/12 + C
b) sin^3(2x)/12 + C
c) -cos^3(2x)/12 + C
d) cos^3(2x)/12 + C
Answer: b) sin^3(2x)/12 + C
62. ∫ sin(2x) cos^2(2x) dx
a) -cos^3(2x)/12 + C
b) cos^3(2x)/12 + C
c) -sin^3(2x)/12 + C
d) sin^3(2x)/12 + C
Answer: a) -cos^3(2x)/12 + C
63. ∫ sin^5 x dx
a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
b) cos x - 2cos^3 x/3 + cos^5 x/5 + C
c) -cos x - 2cos^3 x/3 + cos^5 x/5 + C
d) cos x + 2cos^3 x/3 - cos^5 x/5 + C
Answer: a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
64. ∫ cos^5 x dx
a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
b) -sin x + 2sin^3 x/3 - sin^5 x/5 + C
c) sin x + 2sin^3 x/3 - sin^5 x/5 + C
d) -sin x - 2sin^3 x/3 + sin^5 x/5 + C
Answer: a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
65. ∫ tan^5 x dx
a) ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
c) ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
d) -ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
66. ∫ cot^5 x dx
a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
b) -ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
c) ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
d) -ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
Answer: a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
67. ∫ sec^5 x dx
a) tan x + tan^3 x/3 + tan^5 x/5 + C
b) -tan x - tan^3 x/3 - tan^5 x/5 + C
c) tan x - tan^3 x/3 + tan^5 x/5 + C
d) -tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: a) tan x + tan^3 x/3 + tan^5 x/5 + C
68. ∫ csc^5 x dx
a) -cot x - cot^3 x/3 - cot^5 x/5 + C
b) cot x + cot^3 x/3 + cot^5 x/5 + C
c) -cot x + cot^3 x/3 - cot^5 x/5 + C
d) cot x - cot^3 x/3 + cot^5 x/5 + C
Answer: a) -cot x - cot^3 x/3 - cot^5 x/5 + C
69. ∫ sin(x) cos(x/2) dx
a) -2sin(x/2)/3 - 2sin(3x/2)/3 + C
b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
c) -2sin(x/2)/3 + 2sin(3x/2)/3 + C
d) 2sin(x/2)/3 - 2sin(3x/2)/3 + C
Answer: b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
70. ∫ sin(x/2) cos(x) dx
a) -2cos(x/2)/3 + 2cos(3x/2)/3 + C
b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
c) -2cos(x/2)/3 - 2cos(3x/2)/3 + C
d) 2cos(x/2)/3 + 2cos(3x/2)/3 + C
Answer: b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
71. ∫ sin^2(x) cos^2(x/2) dx
a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
b) 3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
c) -3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
d) -3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
Answer: a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
72. ∫ sin^2(x/2) cos^2(x) dx
a) x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
c) -x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
d) -x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
Answer: b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
55. ∫ tan^4 x dx
a) tan^3 x/3 - tan x + x + C
b) -tan^3 x/3 + tan x - x + C
c) tan^3 x/3 + tan x - x + C
d) -tan^3 x/3 - tan x + x + C
Answer: c) tan^3 x/3 + tan x - x + C
56. ∫ cot^4 x dx
a) -cot^3 x/3 - cot x - x + C
b) cot^3 x/3 + cot x + x + C
c) -cot^3 x/3 + cot x - x + C
d) cot^3 x/3 - cot x + x + C
Answer: a) -cot^3 x/3 - cot x - x + C
57. ∫ sec^4 x dx
a) tan^3 x/3 + tan x + C
b) -tan^3 x/3 - tan x + C
c) tan^3 x/3 - tan x + C
d) -tan^3 x/3 + tan x + C
Answer: a) tan^3 x/3 + tan x + C
58. ∫ csc^4 x dx
a) -cot^3 x/3 - cot x + C
b) cot^3 x/3 + cot x + C
c) -cot^3 x/3 + cot x + C
d) cot^3 x/3 - cot x + C
Answer: a) -cot^3 x/3 - cot x + C
59. ∫ sin(3x) cos(2x) dx
a) -sin(5x)/10 + sin x/6 + C
b) sin(5x)/10 - sin x/6 + C
c) -sin(5x)/10 - sin x/6 + C
d) sin(5x)/10 + sin x/6 + C
Answer: b) sin(5x)/10 - sin x/6 + C
60. ∫ sin(2x) cos(3x) dx
a) -cos(5x)/10 - cos x/4 + C
b) cos(5x)/10 + cos x/4 + C
c) -cos(5x)/10 + cos x/4 + C
d) cos(5x)/10 - cos x/4 + C
Answer: b) cos(5x)/10 + cos x/4 + C
61. ∫ sin^2(2x) cos(2x) dx
a) -sin^3(2x)/12 + C
b) sin^3(2x)/12 + C
c) -cos^3(2x)/12 + C
d) cos^3(2x)/12 + C
Answer: b) sin^3(2x)/12 + C
62. ∫ sin(2x) cos^2(2x) dx
a) -cos^3(2x)/12 + C
b) cos^3(2x)/12 + C
c) -sin^3(2x)/12 + C
d) sin^3(2x)/12 + C
Answer: a) -cos^3(2x)/12 + C
63. ∫ sin^5 x dx
a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
b) cos x - 2cos^3 x/3 + cos^5 x/5 + C
c) -cos x - 2cos^3 x/3 + cos^5 x/5 + C
d) cos x + 2cos^3 x/3 - cos^5 x/5 + C
Answer: a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
64. ∫ cos^5 x dx
a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
b) -sin x + 2sin^3 x/3 - sin^5 x/5 + C
c) sin x + 2sin^3 x/3 - sin^5 x/5 + C
d) -sin x - 2sin^3 x/3 + sin^5 x/5 + C
Answer: a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
65. ∫ tan^5 x dx
a) ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
c) ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
d) -ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
66. ∫ cot^5 x dx
a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
b) -ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
c) ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
d) -ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
Answer: a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
67. ∫ sec^5 x dx
a) tan x + tan^3 x/3 + tan^5 x/5 + C
b) -tan x - tan^3 x/3 - tan^5 x/5 + C
c) tan x - tan^3 x/3 + tan^5 x/5 + C
d) -tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: a) tan x + tan^3 x/3 + tan^5 x/5 + C
68. ∫ csc^5 x dx
a) -cot x - cot^3 x/3 - cot^5 x/5 + C
b) cot x + cot^3 x/3 + cot^5 x/5 + C
c) -cot x + cot^3 x/3 - cot^5 x/5 + C
d) cot x - cot^3 x/3 + cot^5 x/5 + C
Answer: a) -cot x - cot^3 x/3 - cot^5 x/5 + C
69. ∫ sin(x) cos(x/2) dx
a) -2sin(x/2)/3 - 2sin(3x/2)/3 + C
b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
c) -2sin(x/2)/3 + 2sin(3x/2)/3 + C
d) 2sin(x/2)/3 - 2sin(3x/2)/3 + C
Answer: b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
70. ∫ sin(x/2) cos(x) dx
a) -2cos(x/2)/3 + 2cos(3x/2)/3 + C
b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
c) -2cos(x/2)/3 - 2cos(3x/2)/3 + C
d) 2cos(x/2)/3 + 2cos(3x/2)/3 + C
Answer: b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
71. ∫ sin^2(x) cos^2(x/2) dx
a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
b) 3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
c) -3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
d) -3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
Answer: a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
72. ∫ sin^2(x/2) cos^2(x) dx
a) x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
c) -x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
d) -x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
Answer: b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
55. ∫ tan^4 x dx
a) tan^3 x/3 - tan x + x + C
b) -tan^3 x/3 + tan x - x + C
c) tan^3 x/3 + tan x - x + C
d) -tan^3 x/3 - tan x + x + C
Answer: c) tan^3 x/3 + tan x - x + C
56. ∫ cot^4 x dx
a) -cot^3 x/3 - cot x - x + C
b) cot^3 x/3 + cot x + x + C
c) -cot^3 x/3 + cot x - x + C
d) cot^3 x/3 - cot x + x + C
Answer: a) -cot^3 x/3 - cot x - x + C
57. ∫ sec^4 x dx
a) tan^3 x/3 + tan x + C
b) -tan^3 x/3 - tan x + C
c) tan^3 x/3 - tan x + C
d) -tan^3 x/3 + tan x + C
Answer: a) tan^3 x/3 + tan x + C
58. ∫ csc^4 x dx
a) -cot^3 x/3 - cot x + C
b) cot^3 x/3 + cot x + C
c) -cot^3 x/3 + cot x + C
d) cot^3 x/3 - cot x + C
Answer: a) -cot^3 x/3 - cot x + C
59. ∫ sin(3x) cos(2x) dx
a) -sin(5x)/10 + sin x/6 + C
b) sin(5x)/10 - sin x/6 + C
c) -sin(5x)/10 - sin x/6 + C
d) sin(5x)/10 + sin x/6 + C
Answer: b) sin(5x)/10 - sin x/6 + C
60. ∫ sin(2x) cos(3x) dx
a) -cos(5x)/10 - cos x/4 + C
b) cos(5x)/10 + cos x/4 + C
c) -cos(5x)/10 + cos x/4 + C
d) cos(5x)/10 - cos x/4 + C
Answer: b) cos(5x)/10 + cos x/4 + C
61. ∫ sin^2(2x) cos(2x) dx
a) -sin^3(2x)/12 + C
b) sin^3(2x)/12 + C
c) -cos^3(2x)/12 + C
d) cos^3(2x)/12 + C
Answer: b) sin^3(2x)/12 + C
62. ∫ sin(2x) cos^2(2x) dx
a) -cos^3(2x)/12 + C
b) cos^3(2x)/12 + C
c) -sin^3(2x)/12 + C
d) sin^3(2x)/12 + C
Answer: a) -cos^3(2x)/12 + C
63. ∫ sin^5 x dx
a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
b) cos x - 2cos^3 x/3 + cos^5 x/5 + C
c) -cos x - 2cos^3 x/3 + cos^5 x/5 + C
d) cos x + 2cos^3 x/3 - cos^5 x/5 + C
Answer: a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
64. ∫ cos^5 x dx
a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
b) -sin x + 2sin^3 x/3 - sin^5 x/5 + C
c) sin x + 2sin^3 x/3 - sin^5 x/5 + C
d) -sin x - 2sin^3 x/3 + sin^5 x/5 + C
Answer: a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
65. ∫ tan^5 x dx
a) ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
c) ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
d) -ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
66. ∫ cot^5 x dx
a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
b) -ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
c) ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
d) -ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
Answer: a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
67. ∫ sec^5 x dx
a) tan x + tan^3 x/3 + tan^5 x/5 + C
b) -tan x - tan^3 x/3 - tan^5 x/5 + C
c) tan x - tan^3 x/3 + tan^5 x/5 + C
d) -tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: a) tan x + tan^3 x/3 + tan^5 x/5 + C
68. ∫ csc^5 x dx
a) -cot x - cot^3 x/3 - cot^5 x/5 + C
b) cot x + cot^3 x/3 + cot^5 x/5 + C
c) -cot x + cot^3 x/3 - cot^5 x/5 + C
d) cot x - cot^3 x/3 + cot^5 x/5 + C
Answer: a) -cot x - cot^3 x/3 - cot^5 x/5 + C
69. ∫ sin(x) cos(x/2) dx
a) -2sin(x/2)/3 - 2sin(3x/2)/3 + C
b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
c) -2sin(x/2)/3 + 2sin(3x/2)/3 + C
d) 2sin(x/2)/3 - 2sin(3x/2)/3 + C
Answer: b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
70. ∫ sin(x/2) cos(x) dx
a) -2cos(x/2)/3 + 2cos(3x/2)/3 + C
b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
c) -2cos(x/2)/3 - 2cos(3x/2)/3 + C
d) 2cos(x/2)/3 + 2cos(3x/2)/3 + C
Answer: b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
71. ∫ sin^2(x) cos^2(x/2) dx
a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
b) 3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
c) -3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
d) -3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
Answer: a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
72. ∫ sin^2(x/2) cos^2(x) dx
a) x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
c) -x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
d) -x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
Answer: b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
55. ∫ tan^4 x dx
a) tan^3 x/3 - tan x + x + C
b) -tan^3 x/3 + tan x - x + C
c) tan^3 x/3 + tan x - x + C
d) -tan^3 x/3 - tan x + x + C
Answer: c) tan^3 x/3 + tan x - x + C
56. ∫ cot^4 x dx
a) -cot^3 x/3 - cot x - x + C
b) cot^3 x/3 + cot x + x + C
c) -cot^3 x/3 + cot x - x + C
d) cot^3 x/3 - cot x + x + C
Answer: a) -cot^3 x/3 - cot x - x + C
57. ∫ sec^4 x dx
a) tan^3 x/3 + tan x + C
b) -tan^3 x/3 - tan x + C
c) tan^3 x/3 - tan x + C
d) -tan^3 x/3 + tan x + C
Answer: a) tan^3 x/3 + tan x + C
58. ∫ csc^4 x dx
a) -cot^3 x/3 - cot x + C
b) cot^3 x/3 + cot x + C
c) -cot^3 x/3 + cot x + C
d) cot^3 x/3 - cot x + C
Answer: a) -cot^3 x/3 - cot x + C
59. ∫ sin(3x) cos(2x) dx
a) -sin(5x)/10 + sin x/6 + C
b) sin(5x)/10 - sin x/6 + C
c) -sin(5x)/10 - sin x/6 + C
d) sin(5x)/10 + sin x/6 + C
Answer: b) sin(5x)/10 - sin x/6 + C
60. ∫ sin(2x) cos(3x) dx
a) -cos(5x)/10 - cos x/4 + C
b) cos(5x)/10 + cos x/4 + C
c) -cos(5x)/10 + cos x/4 + C
d) cos(5x)/10 - cos x/4 + C
Answer: b) cos(5x)/10 + cos x/4 + C
61. ∫ sin^2(2x) cos(2x) dx
a) -sin^3(2x)/12 + C
b) sin^3(2x)/12 + C
c) -cos^3(2x)/12 + C
d) cos^3(2x)/12 + C
Answer: b) sin^3(2x)/12 + C
62. ∫ sin(2x) cos^2(2x) dx
a) -cos^3(2x)/12 + C
b) cos^3(2x)/12 + C
c) -sin^3(2x)/12 + C
d) sin^3(2x)/12 + C
Answer: a) -cos^3(2x)/12 + C
63. ∫ sin^5 x dx
a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
b) cos x - 2cos^3 x/3 + cos^5 x/5 + C
c) -cos x - 2cos^3 x/3 + cos^5 x/5 + C
d) cos x + 2cos^3 x/3 - cos^5 x/5 + C
Answer: a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
64. ∫ cos^5 x dx
a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
b) -sin x + 2sin^3 x/3 - sin^5 x/5 + C
c) sin x + 2sin^3 x/3 - sin^5 x/5 + C
d) -sin x - 2sin^3 x/3 + sin^5 x/5 + C
Answer: a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
65. ∫ tan^5 x dx
a) ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
c) ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
d) -ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
66. ∫ cot^5 x dx
a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
b) -ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
c) ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
d) -ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
Answer: a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
67. ∫ sec^5 x dx
a) tan x + tan^3 x/3 + tan^5 x/5 + C
b) -tan x - tan^3 x/3 - tan^5 x/5 + C
c) tan x - tan^3 x/3 + tan^5 x/5 + C
d) -tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: a) tan x + tan^3 x/3 + tan^5 x/5 + C
68. ∫ csc^5 x dx
a) -cot x - cot^3 x/3 - cot^5 x/5 + C
b) cot x + cot^3 x/3 + cot^5 x/5 + C
c) -cot x + cot^3 x/3 - cot^5 x/5 + C
d) cot x - cot^3 x/3 + cot^5 x/5 + C
Answer: a) -cot x - cot^3 x/3 - cot^5 x/5 + C
69. ∫ sin(x) cos(x/2) dx
a) -2sin(x/2)/3 - 2sin(3x/2)/3 + C
b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
c) -2sin(x/2)/3 + 2sin(3x/2)/3 + C
d) 2sin(x/2)/3 - 2sin(3x/2)/3 + C
Answer: b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
70. ∫ sin(x/2) cos(x) dx
a) -2cos(x/2)/3 + 2cos(3x/2)/3 + C
b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
c) -2cos(x/2)/3 - 2cos(3x/2)/3 + C
d) 2cos(x/2)/3 + 2cos(3x/2)/3 + C
Answer: b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
71. ∫ sin^2(x) cos^2(x/2) dx
a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
b) 3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
c) -3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
d) -3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
Answer: a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
72. ∫ sin^2(x/2) cos^2(x) dx
a) x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
c) -x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
d) -x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
Answer: b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
55. ∫ tan^4 x dx
a) tan^3 x/3 - tan x + x + C
b) -tan^3 x/3 + tan x - x + C
c) tan^3 x/3 + tan x - x + C
d) -tan^3 x/3 - tan x + x + C
Answer: c) tan^3 x/3 + tan x - x + C
56. ∫ cot^4 x dx
a) -cot^3 x/3 - cot x - x + C
b) cot^3 x/3 + cot x + x + C
c) -cot^3 x/3 + cot x - x + C
d) cot^3 x/3 - cot x + x + C
Answer: a) -cot^3 x/3 - cot x - x + C
57. ∫ sec^4 x dx
a) tan^3 x/3 + tan x + C
b) -tan^3 x/3 - tan x + C
c) tan^3 x/3 - tan x + C
d) -tan^3 x/3 + tan x + C
Answer: a) tan^3 x/3 + tan x + C
58. ∫ csc^4 x dx
a) -cot^3 x/3 - cot x + C
b) cot^3 x/3 + cot x + C
c) -cot^3 x/3 + cot x + C
d) cot^3 x/3 - cot x + C
Answer: a) -cot^3 x/3 - cot x + C
59. ∫ sin(3x) cos(2x) dx
a) -sin(5x)/10 + sin x/6 + C
b) sin(5x)/10 - sin x/6 + C
c) -sin(5x)/10 - sin x/6 + C
d) sin(5x)/10 + sin x/6 + C
Answer: b) sin(5x)/10 - sin x/6 + C
60. ∫ sin(2x) cos(3x) dx
a) -cos(5x)/10 - cos x/4 + C
b) cos(5x)/10 + cos x/4 + C
c) -cos(5x)/10 + cos x/4 + C
d) cos(5x)/10 - cos x/4 + C
Answer: b) cos(5x)/10 + cos x/4 + C
61. ∫ sin^2(2x) cos(2x) dx
a) -sin^3(2x)/12 + C
b) sin^3(2x)/12 + C
c) -cos^3(2x)/12 + C
d) cos^3(2x)/12 + C
Answer: b) sin^3(2x)/12 + C
62. ∫ sin(2x) cos^2(2x) dx
a) -cos^3(2x)/12 + C
b) cos^3(2x)/12 + C
c) -sin^3(2x)/12 + C
d) sin^3(2x)/12 + C
Answer: a) -cos^3(2x)/12 + C
63. ∫ sin^5 x dx
a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
b) cos x - 2cos^3 x/3 + cos^5 x/5 + C
c) -cos x - 2cos^3 x/3 + cos^5 x/5 + C
d) cos x + 2cos^3 x/3 - cos^5 x/5 + C
Answer: a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
64. ∫ cos^5 x dx
a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
b) -sin x + 2sin^3 x/3 - sin^5 x/5 + C
c) sin x + 2sin^3 x/3 - sin^5 x/5 + C
d) -sin x - 2sin^3 x/3 + sin^5 x/5 + C
Answer: a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
65. ∫ tan^5 x dx
a) ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
c) ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
d) -ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
66. ∫ cot^5 x dx
a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
b) -ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
c) ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
d) -ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
Answer: a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
67. ∫ sec^5 x dx
a) tan x + tan^3 x/3 + tan^5 x/5 + C
b) -tan x - tan^3 x/3 - tan^5 x/5 + C
c) tan x - tan^3 x/3 + tan^5 x/5 + C
d) -tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: a) tan x + tan^3 x/3 + tan^5 x/5 + C
68. ∫ csc^5 x dx
a) -cot x - cot^3 x/3 - cot^5 x/5 + C
b) cot x + cot^3 x/3 + cot^5 x/5 + C
c) -cot x + cot^3 x/3 - cot^5 x/5 + C
d) cot x - cot^3 x/3 + cot^5 x/5 + C
Answer: a) -cot x - cot^3 x/3 - cot^5 x/5 + C
69. ∫ sin(x) cos(x/2) dx
a) -2sin(x/2)/3 - 2sin(3x/2)/3 + C
b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
c) -2sin(x/2)/3 + 2sin(3x/2)/3 + C
d) 2sin(x/2)/3 - 2sin(3x/2)/3 + C
Answer: b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
70. ∫ sin(x/2) cos(x) dx
a) -2cos(x/2)/3 + 2cos(3x/2)/3 + C
b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
c) -2cos(x/2)/3 - 2cos(3x/2)/3 + C
d) 2cos(x/2)/3 + 2cos(3x/2)/3 + C
Answer: b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
71. ∫ sin^2(x) cos^2(x/2) dx
a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
b) 3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
c) -3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
d) -3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
Answer: a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
72. ∫ sin^2(x/2) cos^2(x) dx
a) x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
c) -x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
d) -x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
Answer: b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
55. ∫ tan^4 x dx
a) tan^3 x/3 - tan x + x + C
b) -tan^3 x/3 + tan x - x + C
c) tan^3 x/3 + tan x - x + C
d) -tan^3 x/3 - tan x + x + C
Answer: c) tan^3 x/3 + tan x - x + C
56. ∫ cot^4 x dx
a) -cot^3 x/3 - cot x - x + C
b) cot^3 x/3 + cot x + x + C
c) -cot^3 x/3 + cot x - x + C
d) cot^3 x/3 - cot x + x + C
Answer: a) -cot^3 x/3 - cot x - x + C
57. ∫ sec^4 x dx
a) tan^3 x/3 + tan x + C
b) -tan^3 x/3 - tan x + C
c) tan^3 x/3 - tan x + C
d) -tan^3 x/3 + tan x + C
Answer: a) tan^3 x/3 + tan x + C
58. ∫ csc^4 x dx
a) -cot^3 x/3 - cot x + C
b) cot^3 x/3 + cot x + C
c) -cot^3 x/3 + cot x + C
d) cot^3 x/3 - cot x + C
Answer: a) -cot^3 x/3 - cot x + C
59. ∫ sin(3x) cos(2x) dx
a) -sin(5x)/10 + sin x/6 + C
b) sin(5x)/10 - sin x/6 + C
c) -sin(5x)/10 - sin x/6 + C
d) sin(5x)/10 + sin x/6 + C
Answer: b) sin(5x)/10 - sin x/6 + C
60. ∫ sin(2x) cos(3x) dx
a) -cos(5x)/10 - cos x/4 + C
b) cos(5x)/10 + cos x/4 + C
c) -cos(5x)/10 + cos x/4 + C
d) cos(5x)/10 - cos x/4 + C
Answer: b) cos(5x)/10 + cos x/4 + C
61. ∫ sin^2(2x) cos(2x) dx
a) -sin^3(2x)/12 + C
b) sin^3(2x)/12 + C
c) -cos^3(2x)/12 + C
d) cos^3(2x)/12 + C
Answer: b) sin^3(2x)/12 + C
62. ∫ sin(2x) cos^2(2x) dx
a) -cos^3(2x)/12 + C
b) cos^3(2x)/12 + C
c) -sin^3(2x)/12 + C
d) sin^3(2x)/12 + C
Answer: a) -cos^3(2x)/12 + C
63. ∫ sin^5 x dx
a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
b) cos x - 2cos^3 x/3 + cos^5 x/5 + C
c) -cos x - 2cos^3 x/3 + cos^5 x/5 + C
d) cos x + 2cos^3 x/3 - cos^5 x/5 + C
Answer: a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
64. ∫ cos^5 x dx
a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
b) -sin x + 2sin^3 x/3 - sin^5 x/5 + C
c) sin x + 2sin^3 x/3 - sin^5 x/5 + C
d) -sin x - 2sin^3 x/3 + sin^5 x/5 + C
Answer: a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
65. ∫ tan^5 x dx
a) ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
c) ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
d) -ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
66. ∫ cot^5 x dx
a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
b) -ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
c) ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
d) -ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
Answer: a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
67. ∫ sec^5 x dx
a) tan x + tan^3 x/3 + tan^5 x/5 + C
b) -tan x - tan^3 x/3 - tan^5 x/5 + C
c) tan x - tan^3 x/3 + tan^5 x/5 + C
d) -tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: a) tan x + tan^3 x/3 + tan^5 x/5 + C
68. ∫ csc^5 x dx
a) -cot x - cot^3 x/3 - cot^5 x/5 + C
b) cot x + cot^3 x/3 + cot^5 x/5 + C
c) -cot x + cot^3 x/3 - cot^5 x/5 + C
d) cot x - cot^3 x/3 + cot^5 x/5 + C
Answer: a) -cot x - cot^3 x/3 - cot^5 x/5 + C
69. ∫ sin(x) cos(x/2) dx
a) -2sin(x/2)/3 - 2sin(3x/2)/3 + C
b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
c) -2sin(x/2)/3 + 2sin(3x/2)/3 + C
d) 2sin(x/2)/3 - 2sin(3x/2)/3 + C
Answer: b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
70. ∫ sin(x/2) cos(x) dx
a) -2cos(x/2)/3 + 2cos(3x/2)/3 + C
b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
c) -2cos(x/2)/3 - 2cos(3x/2)/3 + C
d) 2cos(x/2)/3 + 2cos(3x/2)/3 + C
Answer: b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
71. ∫ sin^2(x) cos^2(x/2) dx
a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
b) 3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
c) -3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
d) -3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
Answer: a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
72. ∫ sin^2(x/2) cos^2(x) dx
a) x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
c) -x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
d) -x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
Answer: b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
55. ∫ tan^4 x dx
a) tan^3 x/3 - tan x + x + C
b) -tan^3 x/3 + tan x - x + C
c) tan^3 x/3 + tan x - x + C
d) -tan^3 x/3 - tan x + x + C
Answer: c) tan^3 x/3 + tan x - x + C
56. ∫ cot^4 x dx
a) -cot^3 x/3 - cot x - x + C
b) cot^3 x/3 + cot x + x + C
c) -cot^3 x/3 + cot x - x + C
d) cot^3 x/3 - cot x + x + C
Answer: a) -cot^3 x/3 - cot x - x + C
57. ∫ sec^4 x dx
a) tan^3 x/3 + tan x + C
b) -tan^3 x/3 - tan x + C
c) tan^3 x/3 - tan x + C
d) -tan^3 x/3 + tan x + C
Answer: a) tan^3 x/3 + tan x + C
58. ∫ csc^4 x dx
a) -cot^3 x/3 - cot x + C
b) cot^3 x/3 + cot x + C
c) -cot^3 x/3 + cot x + C
d) cot^3 x/3 - cot x + C
Answer: a) -cot^3 x/3 - cot x + C
59. ∫ sin(3x) cos(2x) dx
a) -sin(5x)/10 + sin x/6 + C
b) sin(5x)/10 - sin x/6 + C
c) -sin(5x)/10 - sin x/6 + C
d) sin(5x)/10 + sin x/6 + C
Answer: b) sin(5x)/10 - sin x/6 + C
60. ∫ sin(2x) cos(3x) dx
a) -cos(5x)/10 - cos x/4 + C
b) cos(5x)/10 + cos x/4 + C
c) -cos(5x)/10 + cos x/4 + C
d) cos(5x)/10 - cos x/4 + C
Answer: b) cos(5x)/10 + cos x/4 + C
61. ∫ sin^2(2x) cos(2x) dx
a) -sin^3(2x)/12 + C
b) sin^3(2x)/12 + C
c) -cos^3(2x)/12 + C
d) cos^3(2x)/12 + C
Answer: b) sin^3(2x)/12 + C
62. ∫ sin(2x) cos^2(2x) dx
a) -cos^3(2x)/12 + C
b) cos^3(2x)/12 + C
c) -sin^3(2x)/12 + C
d) sin^3(2x)/12 + C
Answer: a) -cos^3(2x)/12 + C
63. ∫ sin^5 x dx
a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
b) cos x - 2cos^3 x/3 + cos^5 x/5 + C
c) -cos x - 2cos^3 x/3 + cos^5 x/5 + C
d) cos x + 2cos^3 x/3 - cos^5 x/5 + C
Answer: a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
64. ∫ cos^5 x dx
a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
b) -sin x + 2sin^3 x/3 - sin^5 x/5 + C
c) sin x + 2sin^3 x/3 - sin^5 x/5 + C
d) -sin x - 2sin^3 x/3 + sin^5 x/5 + C
Answer: a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
65. ∫ tan^5 x dx
a) ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
c) ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
d) -ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
66. ∫ cot^5 x dx
a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
b) -ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
c) ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
d) -ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
Answer: a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
67. ∫ sec^5 x dx
a) tan x + tan^3 x/3 + tan^5 x/5 + C
b) -tan x - tan^3 x/3 - tan^5 x/5 + C
c) tan x - tan^3 x/3 + tan^5 x/5 + C
d) -tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: a) tan x + tan^3 x/3 + tan^5 x/5 + C
68. ∫ csc^5 x dx
a) -cot x - cot^3 x/3 - cot^5 x/5 + C
b) cot x + cot^3 x/3 + cot^5 x/5 + C
c) -cot x + cot^3 x/3 - cot^5 x/5 + C
d) cot x - cot^3 x/3 + cot^5 x/5 + C
Answer: a) -cot x - cot^3 x/3 - cot^5 x/5 + C
69. ∫ sin(x) cos(x/2) dx
a) -2sin(x/2)/3 - 2sin(3x/2)/3 + C
b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
c) -2sin(x/2)/3 + 2sin(3x/2)/3 + C
d) 2sin(x/2)/3 - 2sin(3x/2)/3 + C
Answer: b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
70. ∫ sin(x/2) cos(x) dx
a) -2cos(x/2)/3 + 2cos(3x/2)/3 + C
b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
c) -2cos(x/2)/3 - 2cos(3x/2)/3 + C
d) 2cos(x/2)/3 + 2cos(3x/2)/3 + C
Answer: b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
71. ∫ sin^2(x) cos^2(x/2) dx
a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
b) 3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
c) -3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
d) -3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
Answer: a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
72. ∫ sin^2(x/2) cos^2(x) dx
a) x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
c) -x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
d) -x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
Answer: b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
55. ∫ tan^4 x dx
a) tan^3 x/3 - tan x + x + C
b) -tan^3 x/3 + tan x - x + C
c) tan^3 x/3 + tan x - x + C
d) -tan^3 x/3 - tan x + x + C
Answer: c) tan^3 x/3 + tan x - x + C
56. ∫ cot^4 x dx
a) -cot^3 x/3 - cot x - x + C
b) cot^3 x/3 + cot x + x + C
c) -cot^3 x/3 + cot x - x + C
d) cot^3 x/3 - cot x + x + C
Answer: a) -cot^3 x/3 - cot x - x + C
57. ∫ sec^4 x dx
a) tan^3 x/3 + tan x + C
b) -tan^3 x/3 - tan x + C
c) tan^3 x/3 - tan x + C
d) -tan^3 x/3 + tan x + C
Answer: a) tan^3 x/3 + tan x + C
58. ∫ csc^4 x dx
a) -cot^3 x/3 - cot x + C
b) cot^3 x/3 + cot x + C
c) -cot^3 x/3 + cot x + C
d) cot^3 x/3 - cot x + C
Answer: a) -cot^3 x/3 - cot x + C
59. ∫ sin(3x) cos(2x) dx
a) -sin(5x)/10 + sin x/6 + C
b) sin(5x)/10 - sin x/6 + C
c) -sin(5x)/10 - sin x/6 + C
d) sin(5x)/10 + sin x/6 + C
Answer: b) sin(5x)/10 - sin x/6 + C
60. ∫ sin(2x) cos(3x) dx
a) -cos(5x)/10 - cos x/4 + C
b) cos(5x)/10 + cos x/4 + C
c) -cos(5x)/10 + cos x/4 + C
d) cos(5x)/10 - cos x/4 + C
Answer: b) cos(5x)/10 + cos x/4 + C
61. ∫ sin^2(2x) cos(2x) dx
a) -sin^3(2x)/12 + C
b) sin^3(2x)/12 + C
c) -cos^3(2x)/12 + C
d) cos^3(2x)/12 + C
Answer: b) sin^3(2x)/12 + C
62. ∫ sin(2x) cos^2(2x) dx
a) -cos^3(2x)/12 + C
b) cos^3(2x)/12 + C
c) -sin^3(2x)/12 + C
d) sin^3(2x)/12 + C
Answer: a) -cos^3(2x)/12 + C
63. ∫ sin^5 x dx
a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
b) cos x - 2cos^3 x/3 + cos^5 x/5 + C
c) -cos x - 2cos^3 x/3 + cos^5 x/5 + C
d) cos x + 2cos^3 x/3 - cos^5 x/5 + C
Answer: a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
64. ∫ cos^5 x dx
a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
b) -sin x + 2sin^3 x/3 - sin^5 x/5 + C
c) sin x + 2sin^3 x/3 - sin^5 x/5 + C
d) -sin x - 2sin^3 x/3 + sin^5 x/5 + C
Answer: a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
65. ∫ tan^5 x dx
a) ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
c) ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
d) -ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
66. ∫ cot^5 x dx
a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
b) -ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
c) ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
d) -ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
Answer: a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
67. ∫ sec^5 x dx
a) tan x + tan^3 x/3 + tan^5 x/5 + C
b) -tan x - tan^3 x/3 - tan^5 x/5 + C
c) tan x - tan^3 x/3 + tan^5 x/5 + C
d) -tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: a) tan x + tan^3 x/3 + tan^5 x/5 + C
68. ∫ csc^5 x dx
a) -cot x - cot^3 x/3 - cot^5 x/5 + C
b) cot x + cot^3 x/3 + cot^5 x/5 + C
c) -cot x + cot^3 x/3 - cot^5 x/5 + C
d) cot x - cot^3 x/3 + cot^5 x/5 + C
Answer: a) -cot x - cot^3 x/3 - cot^5 x/5 + C
69. ∫ sin(x) cos(x/2) dx
a) -2sin(x/2)/3 - 2sin(3x/2)/3 + C
b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
c) -2sin(x/2)/3 + 2sin(3x/2)/3 + C
d) 2sin(x/2)/3 - 2sin(3x/2)/3 + C
Answer: b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
70. ∫ sin(x/2) cos(x) dx
a) -2cos(x/2)/3 + 2cos(3x/2)/3 + C
b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
c) -2cos(x/2)/3 - 2cos(3x/2)/3 + C
d) 2cos(x/2)/3 + 2cos(3x/2)/3 + C
Answer: b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
71. ∫ sin^2(x) cos^2(x/2) dx
a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
b) 3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
c) -3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
d) -3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
Answer: a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
72. ∫ sin^2(x/2) cos^2(x) dx
a) x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
c) -x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
d) -x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
Answer: b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
55. ∫ tan^4 x dx
a) tan^3 x/3 - tan x + x + C
b) -tan^3 x/3 + tan x - x + C
c) tan^3 x/3 + tan x - x + C
d) -tan^3 x/3 - tan x + x + C
Answer: c) tan^3 x/3 + tan x - x + C
56. ∫ cot^4 x dx
a) -cot^3 x/3 - cot x - x + C
b) cot^3 x/3 + cot x + x + C
c) -cot^3 x/3 + cot x - x + C
d) cot^3 x/3 - cot x + x + C
Answer: a) -cot^3 x/3 - cot x - x + C
57. ∫ sec^4 x dx
a) tan^3 x/3 + tan x + C
b) -tan^3 x/3 - tan x + C
c) tan^3 x/3 - tan x + C
d) -tan^3 x/3 + tan x + C
Answer: a) tan^3 x/3 + tan x + C
58. ∫ csc^4 x dx
a) -cot^3 x/3 - cot x + C
b) cot^3 x/3 + cot x + C
c) -cot^3 x/3 + cot x + C
d) cot^3 x/3 - cot x + C
Answer: a) -cot^3 x/3 - cot x + C
59. ∫ sin(3x) cos(2x) dx
a) -sin(5x)/10 + sin x/6 + C
b) sin(5x)/10 - sin x/6 + C
c) -sin(5x)/10 - sin x/6 + C
d) sin(5x)/10 + sin x/6 + C
Answer: b) sin(5x)/10 - sin x/6 + C
60. ∫ sin(2x) cos(3x) dx
a) -cos(5x)/10 - cos x/4 + C
b) cos(5x)/10 + cos x/4 + C
c) -cos(5x)/10 + cos x/4 + C
d) cos(5x)/10 - cos x/4 + C
Answer: b) cos(5x)/10 + cos x/4 + C
61. ∫ sin^2(2x) cos(2x) dx
a) -sin^3(2x)/12 + C
b) sin^3(2x)/12 + C
c) -cos^3(2x)/12 + C
d) cos^3(2x)/12 + C
Answer: b) sin^3(2x)/12 + C
62. ∫ sin(2x) cos^2(2x) dx
a) -cos^3(2x)/12 + C
b) cos^3(2x)/12 + C
c) -sin^3(2x)/12 + C
d) sin^3(2x)/12 + C
Answer: a) -cos^3(2x)/12 + C
63. ∫ sin^5 x dx
a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
b) cos x - 2cos^3 x/3 + cos^5 x/5 + C
c) -cos x - 2cos^3 x/3 + cos^5 x/5 + C
d) cos x + 2cos^3 x/3 - cos^5 x/5 + C
Answer: a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
64. ∫ cos^5 x dx
a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
b) -sin x + 2sin^3 x/3 - sin^5 x/5 + C
c) sin x + 2sin^3 x/3 - sin^5 x/5 + C
d) -sin x - 2sin^3 x/3 + sin^5 x/5 + C
Answer: a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
65. ∫ tan^5 x dx
a) ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
c) ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
d) -ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
66. ∫ cot^5 x dx
a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
b) -ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
c) ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
d) -ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
Answer: a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
67. ∫ sec^5 x dx
a) tan x + tan^3 x/3 + tan^5 x/5 + C
b) -tan x - tan^3 x/3 - tan^5 x/5 + C
c) tan x - tan^3 x/3 + tan^5 x/5 + C
d) -tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: a) tan x + tan^3 x/3 + tan^5 x/5 + C
68. ∫ csc^5 x dx
a) -cot x - cot^3 x/3 - cot^5 x/5 + C
b) cot x + cot^3 x/3 + cot^5 x/5 + C
c) -cot x + cot^3 x/3 - cot^5 x/5 + C
d) cot x - cot^3 x/3 + cot^5 x/5 + C
Answer: a) -cot x - cot^3 x/3 - cot^5 x/5 + C
69. ∫ sin(x) cos(x/2) dx
a) -2sin(x/2)/3 - 2sin(3x/2)/3 + C
b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
c) -2sin(x/2)/3 + 2sin(3x/2)/3 + C
d) 2sin(x/2)/3 - 2sin(3x/2)/3 + C
Answer: b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
70. ∫ sin(x/2) cos(x) dx
a) -2cos(x/2)/3 + 2cos(3x/2)/3 + C
b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
c) -2cos(x/2)/3 - 2cos(3x/2)/3 + C
d) 2cos(x/2)/3 + 2cos(3x/2)/3 + C
Answer: b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
71. ∫ sin^2(x) cos^2(x/2) dx
a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
b) 3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
c) -3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
d) -3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
Answer: a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
72. ∫ sin^2(x/2) cos^2(x) dx
a) x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
c) -x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
d) -x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
Answer: b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
55. ∫ tan^4 x dx
a) tan^3 x/3 - tan x + x + C
b) -tan^3 x/3 + tan x - x + C
c) tan^3 x/3 + tan x - x + C
d) -tan^3 x/3 - tan x + x + C
Answer: c) tan^3 x/3 + tan x - x + C
56. ∫ cot^4 x dx
a) -cot^3 x/3 - cot x - x + C
b) cot^3 x/3 + cot x + x + C
c) -cot^3 x/3 + cot x - x + C
d) cot^3 x/3 - cot x + x + C
Answer: a) -cot^3 x/3 - cot x - x + C
57. ∫ sec^4 x dx
a) tan^3 x/3 + tan x + C
b) -tan^3 x/3 - tan x + C
c) tan^3 x/3 - tan x + C
d) -tan^3 x/3 + tan x + C
Answer: a) tan^3 x/3 + tan x + C
58. ∫ csc^4 x dx
a) -cot^3 x/3 - cot x + C
b) cot^3 x/3 + cot x + C
c) -cot^3 x/3 + cot x + C
d) cot^3 x/3 - cot x + C
Answer: a) -cot^3 x/3 - cot x + C
59. ∫ sin(3x) cos(2x) dx
a) -sin(5x)/10 + sin x/6 + C
b) sin(5x)/10 - sin x/6 + C
c) -sin(5x)/10 - sin x/6 + C
d) sin(5x)/10 + sin x/6 + C
Answer: b) sin(5x)/10 - sin x/6 + C
60. ∫ sin(2x) cos(3x) dx
a) -cos(5x)/10 - cos x/4 + C
b) cos(5x)/10 + cos x/4 + C
c) -cos(5x)/10 + cos x/4 + C
d) cos(5x)/10 - cos x/4 + C
Answer: b) cos(5x)/10 + cos x/4 + C
61. ∫ sin^2(2x) cos(2x) dx
a) -sin^3(2x)/12 + C
b) sin^3(2x)/12 + C
c) -cos^3(2x)/12 + C
d) cos^3(2x)/12 + C
Answer: b) sin^3(2x)/12 + C
62. ∫ sin(2x) cos^2(2x) dx
a) -cos^3(2x)/12 + C
b) cos^3(2x)/12 + C
c) -sin^3(2x)/12 + C
d) sin^3(2x)/12 + C
Answer: a) -cos^3(2x)/12 + C
63. ∫ sin^5 x dx
a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
b) cos x - 2cos^3 x/3 + cos^5 x/5 + C
c) -cos x - 2cos^3 x/3 + cos^5 x/5 + C
d) cos x + 2cos^3 x/3 - cos^5 x/5 + C
Answer: a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
64. ∫ cos^5 x dx
a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
b) -sin x + 2sin^3 x/3 - sin^5 x/5 + C
c) sin x + 2sin^3 x/3 - sin^5 x/5 + C
d) -sin x - 2sin^3 x/3 + sin^5 x/5 + C
Answer: a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
65. ∫ tan^5 x dx
a) ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
c) ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
d) -ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
66. ∫ cot^5 x dx
a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
b) -ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
c) ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
d) -ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
Answer: a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
67. ∫ sec^5 x dx
a) tan x + tan^3 x/3 + tan^5 x/5 + C
b) -tan x - tan^3 x/3 - tan^5 x/5 + C
c) tan x - tan^3 x/3 + tan^5 x/5 + C
d) -tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: a) tan x + tan^3 x/3 + tan^5 x/5 + C
68. ∫ csc^5 x dx
a) -cot x - cot^3 x/3 - cot^5 x/5 + C
b) cot x + cot^3 x/3 + cot^5 x/5 + C
c) -cot x + cot^3 x/3 - cot^5 x/5 + C
d) cot x - cot^3 x/3 + cot^5 x/5 + C
Answer: a) -cot x - cot^3 x/3 - cot^5 x/5 + C
69. ∫ sin(x) cos(x/2) dx
a) -2sin(x/2)/3 - 2sin(3x/2)/3 + C
b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
c) -2sin(x/2)/3 + 2sin(3x/2)/3 + C
d) 2sin(x/2)/3 - 2sin(3x/2)/3 + C
Answer: b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
70. ∫ sin(x/2) cos(x) dx
a) -2cos(x/2)/3 + 2cos(3x/2)/3 + C
b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
c) -2cos(x/2)/3 - 2cos(3x/2)/3 + C
d) 2cos(x/2)/3 + 2cos(3x/2)/3 + C
Answer: b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
71. ∫ sin^2(x) cos^2(x/2) dx
a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
b) 3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
c) -3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
d) -3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
Answer: a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
72. ∫ sin^2(x/2) cos^2(x) dx
a) x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
c) -x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
d) -x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
Answer: b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
55. ∫ tan^4 x dx
a) tan^3 x/3 - tan x + x + C
b) -tan^3 x/3 + tan x - x + C
c) tan^3 x/3 + tan x - x + C
d) -tan^3 x/3 - tan x + x + C
Answer: c) tan^3 x/3 + tan x - x + C
56. ∫ cot^4 x dx
a) -cot^3 x/3 - cot x - x + C
b) cot^3 x/3 + cot x + x + C
c) -cot^3 x/3 + cot x - x + C
d) cot^3 x/3 - cot x + x + C
Answer: a) -cot^3 x/3 - cot x - x + C
57. ∫ sec^4 x dx
a) tan^3 x/3 + tan x + C
b) -tan^3 x/3 - tan x + C
c) tan^3 x/3 - tan x + C
d) -tan^3 x/3 + tan x + C
Answer: a) tan^3 x/3 + tan x + C
58. ∫ csc^4 x dx
a) -cot^3 x/3 - cot x + C
b) cot^3 x/3 + cot x + C
c) -cot^3 x/3 + cot x + C
d) cot^3 x/3 - cot x + C
Answer: a) -cot^3 x/3 - cot x + C
59. ∫ sin(3x) cos(2x) dx
a) -sin(5x)/10 + sin x/6 + C
b) sin(5x)/10 - sin x/6 + C
c) -sin(5x)/10 - sin x/6 + C
d) sin(5x)/10 + sin x/6 + C
Answer: b) sin(5x)/10 - sin x/6 + C
60. ∫ sin(2x) cos(3x) dx
a) -cos(5x)/10 - cos x/4 + C
b) cos(5x)/10 + cos x/4 + C
c) -cos(5x)/10 + cos x/4 + C
d) cos(5x)/10 - cos x/4 + C
Answer: b) cos(5x)/10 + cos x/4 + C
61. ∫ sin^2(2x) cos(2x) dx
a) -sin^3(2x)/12 + C
b) sin^3(2x)/12 + C
c) -cos^3(2x)/12 + C
d) cos^3(2x)/12 + C
Answer: b) sin^3(2x)/12 + C
62. ∫ sin(2x) cos^2(2x) dx
a) -cos^3(2x)/12 + C
b) cos^3(2x)/12 + C
c) -sin^3(2x)/12 + C
d) sin^3(2x)/12 + C
Answer: a) -cos^3(2x)/12 + C
63. ∫ sin^5 x dx
a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
b) cos x - 2cos^3 x/3 + cos^5 x/5 + C
c) -cos x - 2cos^3 x/3 + cos^5 x/5 + C
d) cos x + 2cos^3 x/3 - cos^5 x/5 + C
Answer: a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
64. ∫ cos^5 x dx
a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
b) -sin x + 2sin^3 x/3 - sin^5 x/5 + C
c) sin x + 2sin^3 x/3 - sin^5 x/5 + C
d) -sin x - 2sin^3 x/3 + sin^5 x/5 + C
Answer: a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
65. ∫ tan^5 x dx
a) ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
c) ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
d) -ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
66. ∫ cot^5 x dx
a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
b) -ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
c) ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
d) -ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
Answer: a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
67. ∫ sec^5 x dx
a) tan x + tan^3 x/3 + tan^5 x/5 + C
b) -tan x - tan^3 x/3 - tan^5 x/5 + C
c) tan x - tan^3 x/3 + tan^5 x/5 + C
d) -tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: a) tan x + tan^3 x/3 + tan^5 x/5 + C
68. ∫ csc^5 x dx
a) -cot x - cot^3 x/3 - cot^5 x/5 + C
b) cot x + cot^3 x/3 + cot^5 x/5 + C
c) -cot x + cot^3 x/3 - cot^5 x/5 + C
d) cot x - cot^3 x/3 + cot^5 x/5 + C
Answer: a) -cot x - cot^3 x/3 - cot^5 x/5 + C
69. ∫ sin(x) cos(x/2) dx
a) -2sin(x/2)/3 - 2sin(3x/2)/3 + C
b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
c) -2sin(x/2)/3 + 2sin(3x/2)/3 + C
d) 2sin(x/2)/3 - 2sin(3x/2)/3 + C
Answer: b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
70. ∫ sin(x/2) cos(x) dx
a) -2cos(x/2)/3 + 2cos(3x/2)/3 + C
b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
c) -2cos(x/2)/3 - 2cos(3x/2)/3 + C
d) 2cos(x/2)/3 + 2cos(3x/2)/3 + C
Answer: b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
71. ∫ sin^2(x) cos^2(x/2) dx
a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
b) 3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
c) -3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
d) -3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
Answer: a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
72. ∫ sin^2(x/2) cos^2(x) dx
a) x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
c) -x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
d) -x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
Answer: b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
55. ∫ tan^4 x dx
a) tan^3 x/3 - tan x + x + C
b) -tan^3 x/3 + tan x - x + C
c) tan^3 x/3 + tan x - x + C
d) -tan^3 x/3 - tan x + x + C
Answer: c) tan^3 x/3 + tan x - x + C
56. ∫ cot^4 x dx
a) -cot^3 x/3 - cot x - x + C
b) cot^3 x/3 + cot x + x + C
c) -cot^3 x/3 + cot x - x + C
d) cot^3 x/3 - cot x + x + C
Answer: a) -cot^3 x/3 - cot x - x + C
57. ∫ sec^4 x dx
a) tan^3 x/3 + tan x + C
b) -tan^3 x/3 - tan x + C
c) tan^3 x/3 - tan x + C
d) -tan^3 x/3 + tan x + C
Answer: a) tan^3 x/3 + tan x + C
58. ∫ csc^4 x dx
a) -cot^3 x/3 - cot x + C
b) cot^3 x/3 + cot x + C
c) -cot^3 x/3 + cot x + C
d) cot^3 x/3 - cot x + C
Answer: a) -cot^3 x/3 - cot x + C
59. ∫ sin(3x) cos(2x) dx
a) -sin(5x)/10 + sin x/6 + C
b) sin(5x)/10 - sin x/6 + C
c) -sin(5x)/10 - sin x/6 + C
d) sin(5x)/10 + sin x/6 + C
Answer: b) sin(5x)/10 - sin x/6 + C
60. ∫ sin(2x) cos(3x) dx
a) -cos(5x)/10 - cos x/4 + C
b) cos(5x)/10 + cos x/4 + C
c) -cos(5x)/10 + cos x/4 + C
d) cos(5x)/10 - cos x/4 + C
Answer: b) cos(5x)/10 + cos x/4 + C
61. ∫ sin^2(2x) cos(2x) dx
a) -sin^3(2x)/12 + C
b) sin^3(2x)/12 + C
c) -cos^3(2x)/12 + C
d) cos^3(2x)/12 + C
Answer: b) sin^3(2x)/12 + C
62. ∫ sin(2x) cos^2(2x) dx
a) -cos^3(2x)/12 + C
b) cos^3(2x)/12 + C
c) -sin^3(2x)/12 + C
d) sin^3(2x)/12 + C
Answer: a) -cos^3(2x)/12 + C
63. ∫ sin^5 x dx
a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
b) cos x - 2cos^3 x/3 + cos^5 x/5 + C
c) -cos x - 2cos^3 x/3 + cos^5 x/5 + C
d) cos x + 2cos^3 x/3 - cos^5 x/5 + C
Answer: a) -cos x + 2cos^3 x/3 - cos^5 x/5 + C
64. ∫ cos^5 x dx
a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
b) -sin x + 2sin^3 x/3 - sin^5 x/5 + C
c) sin x + 2sin^3 x/3 - sin^5 x/5 + C
d) -sin x - 2sin^3 x/3 + sin^5 x/5 + C
Answer: a) sin x - 2sin^3 x/3 + sin^5 x/5 + C
65. ∫ tan^5 x dx
a) ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
c) ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
d) -ln|cos x| - tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: b) -ln|cos x| + tan x - tan^3 x/3 + tan^5 x/5 + C
66. ∫ cot^5 x dx
a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
b) -ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
c) ln|sin x| + cot x - cot^3 x/3 + cot^5 x/5 + C
d) -ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
Answer: a) ln|sin x| - cot x + cot^3 x/3 - cot^5 x/5 + C
67. ∫ sec^5 x dx
a) tan x + tan^3 x/3 + tan^5 x/5 + C
b) -tan x - tan^3 x/3 - tan^5 x/5 + C
c) tan x - tan^3 x/3 + tan^5 x/5 + C
d) -tan x + tan^3 x/3 - tan^5 x/5 + C
Answer: a) tan x + tan^3 x/3 + tan^5 x/5 + C
68. ∫ csc^5 x dx
a) -cot x - cot^3 x/3 - cot^5 x/5 + C
b) cot x + cot^3 x/3 + cot^5 x/5 + C
c) -cot x + cot^3 x/3 - cot^5 x/5 + C
d) cot x - cot^3 x/3 + cot^5 x/5 + C
Answer: a) -cot x - cot^3 x/3 - cot^5 x/5 + C
69. ∫ sin(x) cos(x/2) dx
a) -2sin(x/2)/3 - 2sin(3x/2)/3 + C
b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
c) -2sin(x/2)/3 + 2sin(3x/2)/3 + C
d) 2sin(x/2)/3 - 2sin(3x/2)/3 + C
Answer: b) 2sin(x/2)/3 + 2sin(3x/2)/3 + C
70. ∫ sin(x/2) cos(x) dx
a) -2cos(x/2)/3 + 2cos(3x/2)/3 + C
b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
c) -2cos(x/2)/3 - 2cos(3x/2)/3 + C
d) 2cos(x/2)/3 + 2cos(3x/2)/3 + C
Answer: b) 2cos(x/2)/3 - 2cos(3x/2)/3 + C
71. ∫ sin^2(x) cos^2(x/2) dx
a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
b) 3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
c) -3x/8 + sin(x)/8 + sin(2x)/16 + sin(3x)/24 + C
d) -3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
Answer: a) 3x/8 - sin(x)/8 - sin(2x)/16 - sin(3x)/24 + C
72. ∫ sin^2(x/2) cos^2(x) dx
a) x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
c) -x/8 + sin(x)/8 - sin(2x)/16 + sin(3x)/24 + C
d) -x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
Answer: b) x/8 - sin(x)/8 + sin(2x)/16 - sin(3x)/24 + C
73. ∫ sin(x) sin(2x) sin(3x) dx
a) -cos(2x)/8 + cos(4x)/16 - cos(6x)/48 + C
b) cos(2x)/8 - cos(4x)/16 + cos(6x)/48 + C
c) -cos(2x)/8 - cos(4x)/16 + cos(6x)/48 + C
d) cos(2x)/8 + cos
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