The problem is
(x^4) / (sqrt x^10 -2)
I thought I could use U- Substitution first and work it out like that...but that doesn't pan out. Help please this one has me stumped.
Let $\displaystyle x^5=\varphi$
so $\displaystyle d\varphi=5x^4dx$
Giving us
$\displaystyle \frac{-1}{5}\int\frac{d\varphi}{2-\varphi^2}$
Now let $\displaystyle \varphi=\sqrt{2}\tanh(\theta)$
and go from there
EDIT:
I am sorry I misread it, it should be
$\displaystyle \frac{1}{5}\int\frac{d\varphi}{\sqrt{\varphi^2-2}}$
Now let $\displaystyle \varphi=\sqrt{2}\sec(\theta)$