1. ## Evaluate the integral?

Evaluate:
$\int \frac{dx}{(x^6 - a^6 + a^2x^4 - a^4x^2)}$

2. It might help to know:

x^6-a^6+a^2*x^4-a^4*x^2=(x^4-a^4)(x^2+a^2)

3. Originally Posted by sirsosay@gmail.com
It might help to know:

x^6-a^6+a^2*x^4-a^4*x^2=(x^4-a^4)(x^2+a^2)
Thank you!
I am still unable to get this:
Spoiler:
$\frac{1}{8a^5}\ln\left|\frac{x - a}{x + a}\right| - \frac{1}{4a^4}\frac{x}{(x^2 + a^2)} - \frac{1}{2a^5}\arctan\left(\frac{x}{a}\right) + C$

4. \begin{aligned}
(x^4-a^4)(x^2+a^2)&=(x^2-a^2)(x^2+a^2)(x^2+a^2) \\
&=(x-a)(x+a)(x^2+a^2)^2 \end{aligned}

Then partial fraction decomposition :

find b,c,d,e such that :
$\frac{1}{(x-a)(x+a)(x^2+a^2)^2}=\frac{b}{x-a}+\frac{c}{x+a}+\frac{d}{x^2+a^2}+\frac{e}{(x^2+a ^2)^2}$

You should get $b=\frac{1}{8a^5} ~,~ c=\frac{-1}{8a^5} ~,~ d=\frac{-1}{4a^4} ~,~ e=\frac{-1}{2a^2}$