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

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.

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TD
Homework Helper
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?

HallsofIvy
Homework Helper
Swatch said:
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.
TD's hint is best: complete the square!

Compleated the square and everything works. Thanks guys.