# Poor integration technique

1. Oct 23, 2013

### pswongaa

My integration skill is very poor, there a many integral that I can't solve, for example:
$$\int_{0}^{\infty}\frac{\sin^{2n+1} x}{x} dx$$
$$\int_{0}^{\infty}\frac{\cos ax-\cos bx}{x} dx$$
but my friend could solve them very quickly, so may I wonder if there are any books about technique for proper and improper riemann integral? Also what is the best way to master integration?

Last edited by a moderator: Oct 23, 2013
2. Oct 23, 2013

### Staff: Mentor

Something is wrong with your post, the integrals aren't rendering correctly.

Mod note: They're fixed now. They were missing the LaTeX tags and were also malformed. I made corrections, but I'm not 100% certain of what the OP intended.

Last edited by a moderator: Oct 23, 2013
3. Oct 23, 2013

### pswongaa

the integrals themselves are not important, I just want to find a way to improve my integration skill

4. Oct 23, 2013

### Tsunoyukami

Unfortunately the only way to get good (ie. fast and accurate) at integrals is by doing integrals - a lot of them.

By going through the procedure repeatedly you will build a collection of tricks that you will learn how to use and when to apply them.

You should open up any calc book and start doing every integral. When you get stuck ask others or look for solutions or
Hints.

5. Oct 23, 2013

### SteamKing

Staff Emeritus
Some integrals can be solved (they have indefinite integrals which are composed of elementary functions) and there are many more which cannot be solved, although the definite integrals can be shown to be equal to a certain value.

It just so happens that the two examples you chose do not have indefinite integrals which are composed of elementary functions.

6. Oct 26, 2013

### Crake

Integrate! As much as possible.

There's this book that has thousands of exercises in Analysis 1.