1. $\displaystyle \int x \sec^2 x \, dx$ 
2. $\displaystyle \int \frac{\cos \sqrt{x}}{\sqrt{x}} \, dx$
3. $\displaystyle \int x (\ln x)^2 \, dx$
4. $\displaystyle \int \frac{1}{x (\ln x)^2} \, dx$
5. $\displaystyle \int \frac{\ln x}{x^2} \, dx$
6. $\displaystyle \int \frac{(\ln x)^3}{x} \, dx$
7. $\displaystyle \int x^3 e^x \, dx$
8. $\displaystyle \int x^5 e^x \, dx$
10. $\displaystyle \int x^2 \sin x^3 \, dx$
11. $\displaystyle \int \sin 3x \cos 2x \, dx$
12. $\displaystyle \int \sin 2x \cos 4x \, dx$
13. $\displaystyle \int \sqrt{x} \ln x \, dx$
14. $\displaystyle \int \frac{e^{\sqrt{x}}}{\sqrt{x}} \, dx$
15. $\displaystyle \int \cos \sqrt{x} \, dx$
16. $\displaystyle \int \sqrt{x} e^{\sqrt{x}} \, dx$
17. $\displaystyle \int_0^{\pi/2} \theta^2 \sin 2\theta \, d\theta$
18. $\displaystyle \int_0^{\pi/2} x^3 \cos 2x \, dx$
19. $\displaystyle \int_{2/\sqrt{3}}^2 t \sec^{-1} t \, dt$
20. $\displaystyle \int_0^{1/\sqrt{2}} 2x \sin^{-1} (x^2) \, dx$
21. $\displaystyle \int x \tan^{-1} x \, dx$
22. $\displaystyle \int x^2 \tan^{-1} \frac{x}{2} \, dx$
23. $\displaystyle \int \frac{dx}{\sqrt{9+x^2}}$
24. $\displaystyle \int \frac{3 \, dx}{\sqrt{1+9x^2}}$
25. $\displaystyle \int_{-2}^2 \frac{dx}{4+x^2}$
26. $\displaystyle \int_0^2 \frac{dx}{8+2x^2}$
27. $\displaystyle \int_0^{3/2} \frac{dx}{\sqrt{9-x^2}}$
28. $\displaystyle \int_0^{1/2\sqrt{2}} \frac{2 \, dx}{\sqrt{1-4x^2}}$
29. $\displaystyle \int \sqrt{25-t^2} \, dt$
30. $\displaystyle \int \frac{dx}{\sqrt{4x^2-49}}, \quad x > \frac{7}{2}$
31. $\displaystyle \int \frac{5 \, dx}{\sqrt{25x^2-9}}, \quad x > \frac{3}{5}$
32. $\displaystyle \int \frac{\sqrt{y^2-49}}{y} \, dy, \quad y > 7$
33. $\displaystyle \int \frac{\sqrt{y^2-25}}{y^3} \, dy, \quad y > 5$
34. $\displaystyle \int \frac{dx}{x^2 \sqrt{x^2-1}}, \quad x > 1$
35. $\displaystyle \int \frac{2 \, dx}{x^3 \sqrt{x^2-1}}, \quad x > 1$
36. $\displaystyle \int \sqrt{1-9t^2} \, dt$
37. $\displaystyle \int \frac{dx}{x\sqrt{x-3}}$
39. $\displaystyle \int \frac{x \, dx}{\sqrt{x-2}}$
40. $\displaystyle \int \frac{x \, dx}{(2x+3)^{3/2}}$
41. $\displaystyle \int \sqrt{2x-3} \, dx$
42. $\displaystyle \int \frac{\sqrt{9-4x}}{x^2} \, dx$
43. $\displaystyle \int \frac{x^2}{\sqrt{4x-9}} \, dx$
44. $\displaystyle \int \sqrt{4x-x^2} \, dx$
45. $\displaystyle \int \sqrt{\frac{x-x^2}{x}} \, dx$
46. $\displaystyle \int \frac{dx}{\sqrt{7+x^2}}$
47. $\displaystyle \int \frac{dx}{\sqrt{7-x^2}}$
48. $\displaystyle \int \frac{\sqrt{4-x^2}}{x} \, dx$
49. $\displaystyle \int \sqrt{x^2-4} \, dx$
50. $\displaystyle \int e^{2t} \cos 3t \, dt$
51. $\displaystyle \int e^{-3t} \sin 4t \, dt$
52. $\displaystyle \int x \cos^{-1} x \, dx$
53. $\displaystyle \int x \tan^{-1} x \, dx$
54. $\displaystyle \int x^2 \tan^{-1} x \, dx$
55. $\displaystyle \int \frac{\tan^{-1} x}{x^2} \, dx$
56. $\displaystyle \int \sin 3x \cos 2x \, dx$
57. $\displaystyle \int \sin 2x \cos 3x \, dx$
58. $\displaystyle \int 8 \sin 4t \sin \frac{t}{2} \, dt$
59. $\displaystyle \int \sin \frac{t}{3} \sin \frac{t}{6} \, dt$
60. $\displaystyle \int \cos \frac{\theta}{3} \cos \frac{\theta}{4} \, d\theta$
61. $\displaystyle \int \cos \frac{\theta}{2} \cos 7\theta \, d\theta$
62. $\displaystyle \int (7x+5)^{3/2} \, dx$
63. $\displaystyle \int_0^{\pi/2} \tan \theta \, d\theta$
64. $\displaystyle \int_0^{\pi/2} \cot \theta \, d\theta$
65. $\displaystyle \int_0^1 \frac{\ln x}{x^2} \, dx$
66. $\displaystyle \int_1^2 \frac{dx}{x \ln x}$
67. $\displaystyle \int_0^{\ln 2} x^{-2} e^{-1/x} \, dx$
68. $\displaystyle \int_0^1 \frac{e^{-\sqrt{x}}}{\sqrt{x}} \, dx$
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