Basic Trigonometric Integration Questions

1. Integrate: \( \int \sin(x) \, dx \)
2. Integrate: \( \int \cos(x) \, dx \)
3. Integrate: \( \int \tan(x) \, dx \)
4. Integrate: \( \int \cot(x) \, dx \)
5. Integrate: \( \int \sec(x) \, dx \)
6. Integrate: \( \int \csc(x) \, dx \)
7. Integrate: \( \int \sin^2(x) \, dx \)
8. Integrate: \( \int \cos^2(x) \, dx \)
9. Integrate: \( \int \sec^2(x) \, dx \)
10. Integrate: \( \int \csc^2(x) \, dx \)
11. Integrate: \( \int \sin^3(x) \, dx \)
12. Integrate: \( \int \cos^3(x) \, dx \)
13. Integrate: \( \int \sec^3(x) \tan(x) \, dx \)
14. Integrate: \( \int \csc^3(x) \cot(x) \, dx \)
15. Integrate: \( \int \sin(x) \cos(x) \, dx \)

Basic Trigonometric Integration Questions and Solutions

1. Integrate: \( \int \sin(x) \, dx \)
   Solution: \( -\cos(x) + C \)
2. Integrate: \( \int \cos(x) \, dx \)
   Solution: \( \sin(x) + C \)
3. Integrate: \( \int \tan(x) \, dx \)
   Solution: \( -\ln|\cos(x)| + C \) or \( \ln|\sec(x)| + C \)
4. Integrate: \( \int \cot(x) \, dx \)
   Solution: \( \ln|\sin(x)| + C \)
5. Integrate: \( \int \sec(x) \, dx \)
   Solution: \( \ln|\sec(x) + \tan(x)| + C \)
6. Integrate: \( \int \csc(x) \, dx \)
   Solution: \( -\ln|\csc(x) + \cot(x)| + C \)
7. Integrate: \( \int \sin^2(x) \, dx \)
   Solution: \( \frac{1}{2} x – \frac{1}{4} \sin(2x) + C \)
8. Integrate: \( \int \cos^2(x) \, dx \)
   Solution: \( \frac{1}{2} x + \frac{1}{4} \sin(2x) + C \)
9. Integrate: \( \int \sec^2(x) \, dx \)
   Solution: \( \tan(x) + C \)
10. Integrate: \( \int \csc^2(x) \, dx \)
    Solution: \( -\cot(x) + C \)
11. Integrate: \( \int \sin^3(x) \, dx \)
    Solution: \( -\frac{1}{3} \cos^3(x) + C \)
12. Integrate: \( \int \cos^3(x) \, dx \)
    Solution: \( \frac{1}{3} \sin^3(x) + C \)
13. Integrate: \( \int \sec^3(x) \tan(x) \, dx \)
    Solution: \( \frac{1}{2} \sec^2(x) + C \)
14. Integrate: \( \int \csc^3(x) \cot(x) \, dx \)
    Solution: \( -\frac{1}{2} \csc^2(x) + C \)
15. Integrate: \( \int \sin(x) \cos(x) \, dx \)
    Solution: \( \frac{1}{2} \sin^2(x) + C \) or using substitution: \( \frac{1}{2} \cos^2(x) + C \)