Trigonometric Integrals

Evaluate each of the following integrals.

1. \( \displaystyle \int \tan(x) \, \mathrm{d}x \)

   Solution
2. \( \displaystyle \int \sec(x) \, \mathrm{d}x \)

   Solution
3. \( \displaystyle \int \cos^2 (x) \, \mathrm{d}x \)

   Solution
4. \( \displaystyle \int \cos^3 (x) \, \mathrm{d}x \)

   Solution
5. \( \displaystyle \int \sin^4(x) \, \mathrm{d}x \)

   Solution
6. \( \displaystyle \int \sin^3(x) \cos^3(x) \, \mathrm{d}x \)

   Solution
7. \( \displaystyle \int \sin^{13}(2x) \cos^3(2x) \, \mathrm{d}x \)

   Solution
8. \( \displaystyle \int \sin^3(x) \cos^4(x) \, \mathrm{d}x \)

   Solution
9. \( \displaystyle \int \sin^{30}(x) \cos^5(x) \, \mathrm{d}x \)

   Solution
10. \( \displaystyle{\int_0^{\pi/2} \sin^2(x) \cos^2(x) \, \mathrm{d}x }\)

    Solution
11. \( \displaystyle \int \tan^2(x) \sec^2(x) \, \mathrm{d}x \)

    Solution
12. \( \displaystyle \int \tan^3(x) \sec^3(x) \, \mathrm{d}x \)

    Solution
13. \( \displaystyle \int \tan^{36}(x) \sec^4(x) \, \mathrm{d}x \)

    Solution
14. \( \displaystyle \int \tan^3(x) \sec^{11}(x) \, \mathrm{d}x \)

    Solution
15. \( \displaystyle \int 4 \tan^{3}(2x) \sec^{17}(2x) \, \mathrm{d}x \)

    Solution
16. \( \displaystyle \int \tan^4(x) \sec^4(x) \, \mathrm{d}x \)

    Solution
17. \( \displaystyle \int \tan^3(x) \, \mathrm{d}x \)

    Solution
18. \( \displaystyle \int 5(\tan^2(x)+ \tan^4(x)) \, \mathrm{d}x \)

    Solution
19. \( \displaystyle \int \sec^3 (x) \, \mathrm{d}x \)

    Solution
20. \( \displaystyle \int \tan^2(x)\sec(x) \, \mathrm{d}x \)

    Solution
21. \(\displaystyle \int 15 \sin^4 (2x) \, \mathrm{d}x \)

    Solution