# Integral Question

• Sep 16th 2009, 10:29 AM
Sprintz
Integral Question
I asked this in an earlier question, but it was overlooked.

2) xdx/x^4 + x^2 + 1

I set u = x^2
du = 2x
= 1/2 Integral of du/u^2+u+1

And I STILL can't solve it!

I want to isolate U^2+1 to make that arctan(u), but I don't see a way.

Cheers!
• Sep 16th 2009, 10:46 AM
running-gag
Hi

Use the "canonical" form
u²+u+1 = (u+1/2)²+3/4

Set t=u+1/2 then v=2t/sqrt(3)
• Sep 16th 2009, 11:38 AM
Krizalid
$\frac{x}{x^{4}+x^{2}+1}=\frac{4x}{\left( 2x^{2}+1 \right)^{2}+3},$ so put $2x^2+1=\sqrt3t$ and you'll get the arctan form.