Complex Integral Calculus Question
Bank – Questions and Answers
Evaluate and Find the answers/solutions for the following
integrals:
1. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
2. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
3. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
4. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
5. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
6. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
7. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
8. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
9. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
10. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
11. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
12. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
13. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
14. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
15. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
16. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
17. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
18. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
19. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
20. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
21. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
22. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
23. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
24. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
25. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
26. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
27. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
28. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
29. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
30. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
31. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
32. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
33. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
34. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
35. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
36. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
37. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
38. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
39. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
40. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
41. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
42. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
43. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
44. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
45. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
46. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
47. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
48. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
49. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
50. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
51. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
52. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
53. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
54. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
55. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
56. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
57. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
58. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
59. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
60. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
61. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
62. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
63. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
64. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
65. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
66. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
67. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
68. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
69. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
70. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
71. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
72. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
73. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
74. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
75. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
76. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
77. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
78. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
79. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
80. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
81. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
82. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
83. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
84. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
85. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
86. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
87. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
88. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
89. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
90. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
91. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
92. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
93. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
94. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
95. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
96. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
97. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
98. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
99. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
100. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
101. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
102. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
103. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
104. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
105. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
106. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
107. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
108. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
109. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
110. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
111. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
112. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
113. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
114. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
115. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
116. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
117. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
118. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
119. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
120. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
121. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
122. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
123. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
124. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
125. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
126. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
127. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
128. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
129. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
130. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
131. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
132. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
133. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
134. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
135. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
136. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
137. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
138. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
139. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
140. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
141. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
142. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
143. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
144. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
145. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
146. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
147. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
148. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
149. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
150. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
151. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
152. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
153. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
154. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
155. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
156. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
157. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
158. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
159. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
160. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
161. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
162. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
163. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
164. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
165. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
166. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
167. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
168. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
169. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
170. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
171. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
172. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
173. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
174. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
175. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
176. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
177. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
178. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
179. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
180. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
181. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
182. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
183. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
184. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
185. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
186. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
187. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
188. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
189. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
190. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
191. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
192. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
193. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
194. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
195. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
196. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
197. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
198. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
199. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
200. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
201. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
202. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
203. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
204. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
205. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
206. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
207. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
208. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
209. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
210. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
211. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
212. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
213. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
214. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
215. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
216. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
217. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
218. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
219. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
220. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
221. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
222. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
223. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
224. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
225. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
226. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
227. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
228. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
229. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
230. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
231. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
232. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
233. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
234. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
235. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
236. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
237. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
238. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
239. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
240. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
241. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
242. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
243. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
244. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
245. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
246. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
247. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
248. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
249. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
250. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
251. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
252. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
253. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
254. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
255. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
256. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
257. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
258. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
259. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
260. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
261. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
262. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
263. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
264. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
265. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
266. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
267. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
268. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
269. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
270. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
271. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
272. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
273. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
274. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
275. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
276. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
277. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
278. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
279. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
280. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
281. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
282. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
283. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
284. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
285. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
286. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
287. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
288. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
289. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
290. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
291. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
292. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
293. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
294. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
295. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
296. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
297. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
298. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
299. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
300. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
301. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
302. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
303. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
304. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
305. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
306. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
307. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
308. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
309. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
310. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
311. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
312. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
313. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
314. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
315. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
316. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
317. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
318. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
319. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
320. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
321. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
322. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
323. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
324. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
325. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
326. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
327. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
328. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
329. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
330. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
331. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
332. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
333. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
334. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
335. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
336. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
337. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
338. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
339. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
340. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
341. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
342. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
343. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
344. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
345. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
346. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
347. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
348. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
349. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
350. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
351. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
352. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
353. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
354. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
355. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
356. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
357. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
358. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
359. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
360. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
361. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
362. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
363. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
364. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
365. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
366. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
367. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
368. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
369. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
370. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
371. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
372. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
373. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
374. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
375. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
376. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
377. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
378. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
379. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
380. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
381. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
382. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
383. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
384. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
385. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
386. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
387. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
388. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
389. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
390. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
391. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
392. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
393. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
394. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
395. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
396. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
397. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
398. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
399. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
400. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
401. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
402. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
403. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
404. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
405. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
406. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
407. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
408. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
409. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
410. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
411. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
412. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
413. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
414. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
415. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
416. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
417. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
418. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
419. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
420. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
421. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
422. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
423. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
424. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
425. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
426. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
427. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
428. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
429. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
430. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
431. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
432. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
433. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
434. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
435. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
436. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
437. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
438. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
439. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
440. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
441. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
442. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
443. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
444. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
445. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
446. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
447. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
448. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
449. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
450. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
451. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
452. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
453. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
454. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
455. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
456. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
457. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
458. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
459. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
460. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
461. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
462. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
463. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
464. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
465. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
466. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
467. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
468. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
469. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
470. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
471. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
472. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
473. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
474. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
475. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
476. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
477. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
478. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
479. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
480. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
481. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
482. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
483. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
484. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
485. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
486. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
487. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
488. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
489. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
490. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
491. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
492. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
493. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
494. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
495. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
496. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
497. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
498. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
499. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
500. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
501. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
502. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
503. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
504. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
505. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
506. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
507. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
508. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
509. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
510. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
511. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
512. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
513. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
514. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
515. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
516. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
517. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
518. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
519. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
520. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
521. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
522. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
523. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
524. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
525. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
526. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
527. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
528. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
529. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
530. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
531. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
532. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
533. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
534. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
535. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
536. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
537. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
538. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
539. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
540. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
541. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
542. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
543. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
544. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
545. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
546. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
547. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
548. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
549. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
550. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
551. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
552. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
553. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
554. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
555. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
556. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
557. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
558. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
559. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
560. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
561. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
562. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
563. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
564. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
565. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
566. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
567. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
568. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
569. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
570. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
571. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
572. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
573. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
574. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
575. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
576. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
577. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
578. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
579. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
580. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
581. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
582. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
583. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
584. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
585. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
586. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
587. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
588. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
589. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
590. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
591. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
592. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
593. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
594. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
595. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
596. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
597. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
598. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
599. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
600. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
601. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
602. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
603. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
604. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
605. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
606. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
607. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
608. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
609. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
610. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
611. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
612. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
613. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
614. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
615. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
616. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
617. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
618. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
619. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
620. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
621. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
622. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
623. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
624. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
625. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
626. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
627. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
628. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
629. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
630. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
631. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
632. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
633. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
634. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
635. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
636. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
637. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
638. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
639. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
640. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
641. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
642. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
643. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
644. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
645. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
646. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
647. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
648. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
649. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
650. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
651. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
652. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
653. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
654. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
655. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
656. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
657. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
658. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
659. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
660. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
661. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
662. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
663. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
664. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
665. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
666. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
667. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
668. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
669. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
670. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
671. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
672. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
673. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
674. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
675. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
676. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
677. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
678. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
679. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
680. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
681. ∫𝑒𝑥 𝑑𝑥
Answer: 𝑒𝑥+ 𝐶
682. ∫𝑥2 𝑑𝑥
Answer: 𝑥3
3+ 𝐶
683. ∫𝑠𝑖𝑛𝑥 𝑑𝑥
Answer: −𝑐𝑜𝑠𝑥 + 𝐶
684. ∫1
𝑥 𝑑𝑥
Answer: 𝑙𝑛|𝑥|+ 𝐶
685. ∫1
1+𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
686. ∫2𝑥 𝑑𝑥
Answer: 𝑥2+ 𝐶
687. ∫1
√1−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥)+ 𝐶
688. ∫𝑐𝑜𝑠𝑥 𝑑𝑥
Answer: 𝑠𝑖𝑛𝑥 + 𝐶
689. ∫𝑥
√1+𝑥2 𝑑𝑥
Answer: √1 + 𝑥2+ 𝐶
690. ∫1
√𝑥 𝑑𝑥
Answer: 2√𝑥 + 𝐶
691. ∫𝑥2
2 𝑑𝑥
Answer: 𝑥3
6+ 𝐶
692. ∫𝑒2𝑥 𝑑𝑥
Answer: 𝑒2𝑥
2+ 𝐶
693. ∫𝑥2+1
𝑥 𝑑𝑥
Answer: 𝑥2
2+ 𝑥 + 𝐶
694. ∫𝑐𝑜𝑠(2𝑥) 𝑑𝑥
Answer: 1
2𝑠𝑖𝑛(2𝑥)+ 𝐶
695. ∫1
√4−𝑥2 𝑑𝑥
Answer: 𝑎𝑟𝑐𝑠𝑖𝑛(𝑥
2) + 𝐶
696. ∫1
√𝑥2+1 𝑑𝑥
Answer: 𝑙𝑛(𝑥 + √𝑥2+ 1) + 𝐶
697. ∫1
𝑥𝑙𝑛𝑥 𝑑𝑥
Answer: 𝑙𝑛(𝑙𝑛𝑥)+ 𝐶
698. ∫𝑠𝑒𝑐2𝑥 𝑑𝑥
Answer: 𝑡𝑎𝑛𝑥 + 𝐶
699. ∫1
1−𝑥2 𝑑𝑥
Answer: 1
2𝑙𝑛|1+𝑥
1−𝑥| + 𝐶
700. ∫𝑥2
1+𝑥2 𝑑𝑥
Answer: 𝑥 − 𝑎𝑟𝑐𝑡𝑎𝑛(𝑥)+ 𝐶
