# Integrate x/(x^2 + ax + a^2)

1. Oct 31, 2005

### Swatch

Hi. I want to integrate x/(x^2 + ax + a^2)
I tried substitution with u=x^2 then du =2x but that didn't work out neither did the substitution x^2 + ax
I thought of factorizing the denominator and using partial fractions, but I think that's not the way, can't figure out the factorization.
Could someone please give me a hint how to integrate this.

Last edited: Oct 31, 2005
2. Oct 31, 2005

### TD

If there was a 2ax in the denominator instead of ax, it would've been easier
This is a typical example of an integral which will have an ln-part and an arctan-part. Do you see why/how?

3. Oct 31, 2005

### HallsofIvy

Staff Emeritus
TD's hint is best: complete the square!

4. Nov 1, 2005

### Swatch

Compleated the square and everything works. Thanks guys.