Trigonometric Integrals

Evaluate each of the following integrals.

General Forms

• \( \displaystyle \int \sin^m (x) \cos^n(x) \, dx\) (General Form) Watch Solution ↗
• \( \displaystyle\int \tan^m(x) \sec^n(x) \, dx\) (General Form) Watch Solution ↗

Practice Problems

1. \( \displaystyle \int \tan(x) \, dx \) Watch Solution ↗
2. \( \displaystyle \int \sec(x) \, dx \) Watch Solution ↗
3. \( \displaystyle \int \cos^2 (x) \, dx \) Watch Solution ↗
4. \( \displaystyle \int \cos^3 (x) \, dx \) Watch Solution ↗
5. \( \displaystyle \int \sin^4(x) \, dx \) Watch Solution ↗
6. \( \displaystyle \int \sin^3(x) \cos^3(x) \, dx \) Watch Solution ↗
7. \( \displaystyle \int \sin^{13}(2x) \cos^3(2x) \, dx \) Watch Solution ↗
8. \( \displaystyle \int \sin^3(x) \cos^4(x) \, dx \) Watch Solution ↗
9. \( \displaystyle \int \sin^{30}(x) \cos^5(x) \, dx \) Watch Solution ↗
10. \( \displaystyle{\int_0^{\pi/2} \sin^2(x) \cos^2(x) \, dx }\) Watch Solution ↗
11. \( \displaystyle \int \tan^2(x) \sec^2(x) \, dx \) Watch Solution ↗
12. \( \displaystyle \int \tan^3(x) \sec^3(x) \, dx \) Watch Solution ↗
13. \( \displaystyle \int \tan^{36}(x) \sec^4(x) \, dx \) Watch Solution ↗
14. \( \displaystyle \int \tan^3(x) \sec^{11}(x) \, dx \) Watch Solution ↗
15. \( \displaystyle \int 4 \tan^{3}(2x) \sec^{17}(2x) \, dx \) Watch Solution ↗
16. \( \displaystyle \int \tan^4(x) \sec^4(x) \, dx \) Watch Solution ↗
17. \( \displaystyle \int \tan^3(x) \, dx \) Watch Solution ↗
18. \( \displaystyle \int 5(\tan^2(x)+ \tan^4(x)) \, dx \) Watch Solution ↗
19. \( \displaystyle \int \sec^3 (x) \, dx \) Watch Solution ↗
20. \( \displaystyle \int \tan^2(x)\sec(x) \, dx \) Watch Solution ↗
21. \(\displaystyle \int 15 \sin^4 (2x) \, dx \) Watch Solution ↗