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