Trigonometric Integrals: Evaluate the following integrals

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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