Solve My Integral

Evaluate the following integral!

1. $ int sin ax dx$
2. $ int cos ax dx $
3. $ int ln (x) dx $
4. $ int e^{2x} $

The following is a list of the integral questions and solutions that are good for you to know. The problem and settlement, the admin got from discussions with friends in Facebook math groups. Do not forget to like facebook admin page (Facebook page: FP Online Maths School). 

1. $ int frac{sin^2(x)cos(x)}{sin(x)+cos(x)} dx$

2. $ int ln |x+ sqrt{x^2+a^2}| dx$

3. $ int_0^{infty} frac{sin^3(x)}{x} dx$

4. $ int cos^{-1}( frac{1-x^2}{1+x^2}) dx$

5. $ int_1^2 e^x ( frac{1}{x} - frac{1}{x^2} ) dx$

6. $ int frac{sin^{-1}( sqrt{x}) - cos^{-1}( sqrt{x} )}{sin^{-1}( sqrt{x}) + cos^{-1}( sqrt{x} )} dx$

7. $  int_0^{ pi} frac{cos(nx)}{2-cos(x)} dx$

8. $ int_0^{infty} frac{1}{1+e^x} dx$

9. $ int frac{sin^3(x)+cos^3(x)}{1+sin^4(x)+cos^4(x)} dx$

10. $ int_0^{frac{1}{2 sqrt{2}}} frac{t^2ln(t)}{ sqrt{t+1}} dt$

If you have good integral questions to share here, please send them to us via the fb mesengger in the box at the bottom corner of this blog!

Can you work on the following integral questions?