Trigonometric Integrals

Evaluate the following integrals

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

2. \( \int \sec(x) \ \mathrm{d}x \)  solution

3. \( \int \sin^m (x) \cos^n(x)\ \mathrm{d}x\)  (general form)    Click Me

4. \( \int \cos^2 (x) \ \mathrm{d}x \)  solution

5. \( \int \cos^3 (x) \ \mathrm{d}x \)  solution

6. \( \int \sin^4(x) \ \mathrm{d}x \)  solution

7. \( \int \sin^3(x) \cos^3(x) \ \mathrm{d}x \)  solution

8. \( \int \sin^{13}(2x) \cos^3(2x) \ \mathrm{d}x \)  solution

9. \( \int \sin^3(x) \cos^4(x) \ \mathrm{d}x \)  solution

10. \( \int \sin^{30}(x) \cos^5(x) \ \mathrm{d}x \) solution

11. \( \displaystyle{\int_0^{\pi/2} \sin^2(x) \cos^2(x) \ \mathrm{d}x }\) solution

12. \( \int \tan^m(x) \sec^n(x)\ \mathrm{d}x\)   (general form)    Click me

13. \( \int \tan^2(x) \sec^2(x) \ \mathrm{d}x \)  solution

14. \( \int \tan^3(x) \sec^3(x) \ \mathrm{d}x \)  solution

15. \( \int \tan^{36}(x) \sec^4(x) \ \mathrm{d}x \)  solution

16. \( \int \tan^3(x) \sec^{11}(x) \ \mathrm{d}x \)  solution

17. \( \int 4 \tan^{3}(2x) \sec^{17}(2x) \ \mathrm{d}x \)  solution

18. \( \int \tan^4(x) \sec^4(x) \ \mathrm{d}x \)  solution

19. \( \int \tan^3(x) \ \mathrm{d}x \)  solution

20. \( \int 5(\tan^2(x)+ \tan^4(x)) \ \mathrm{d}x \) solution

21. \( \int \sec^3 (x) \ \mathrm{d}x \)  solution

22. \( \int \tan^2(x)\sec(x) \ \mathrm{d}x \)   solution

23.\(\int 15 \sin^4 (2x)\ \mathrm{d}x \)  solution