Find an anti derivative (or integral) of the following functions by the method of inspection.

1. \sin 2x

2. \cos 3x

3. e^{2x}

4. (ax + b)^2

5. \sin 2x – 4 e^3x

Find the following integrals in Exercise 6 to 20:

6. \int (4 e^3x+1) dx

7. \int x^2(1-\frac{1}{x^2}) dx

8. \int (ax^2+bx+c) dx

9. \int (2x^2+e^x) dx

10. \int (\sqrt{x}-\frac{1}{\sqrt{x}})^2 dx

11. \int \frac{x^3+5x^2-4}{x^2} dx

12. \int \frac{x^3+3x+4}{\sqrt{x}} dx

13. \int \frac{x^3-x^2+x-1}{x-1} dx

14. \int (1-x)\sqrt{x} dx

15. \int \sqrt{x}(3x^2+2x+3) dx

16. \int (2x-3\cos x+e^x) dx

17. \int (2x^2-3\sin x+5\sqrt{x}) dx

18. \int \sec x ( \sec x+\tan x) dx

19. \int \frac{\sec^2 x}{\cosec^2 x} dx

20. \int \frac{2-3\sin x}{\cos^2 x} dx

21. The anti derivative of (\sqrt{x}+\frac{1}{\sqrt{x}}) equals

22. If \frac{d}{dx}f(x)=4x^3-\frac{3}{x^4} such that f(2)=0 , Then f(x) is