# Indefinite integral

• February 13th 2011, 11:52 AM
Ant
Indefinite integral
Hi,

I'm trying to integrate:

$1/(ax - x^3)$

I've tried using partial fractions; and I've got (1/a) lnx and a^(-3/2) tanh(x/a).

Thanks for any help!
• February 13th 2011, 12:04 PM
Krizalid
substitute $x=\dfrac 1t$ and the integral becomes $\displaystyle-\int{\frac{t}{a{{t}^{2}}-1}\,dt}=-\frac{1}{2a}\ln \left| 1-a{{t}^{2}} \right|+k,$ so back substitute and get $-\dfrac{1}{2a}\ln \left| \dfrac{{{x}^{2}}-a}{{{x}^{2}}} \right|+k.$