How would you to integrate:
1/[x^2* ((1+x^3)^(2/3))]
Thanks
$\displaystyle \int \frac{1}{x^2(1+x^3)^{\frac{2}{3}}}~dx$
Subbing $\displaystyle u = \frac{1}{x} \implies du = -\frac{1}{x^2}~dx$ switches the integral to:
$\displaystyle -\int \frac{1}{(1+\frac{1}{u^3})^{\frac{2}{3}}}~du=-\int \frac{1}{(\frac{u^3+1}{u^3})^{\frac{2}{3}}}~du = -\int \frac{u^2}{(u^3+1)^{\frac{2}{3}}}~du $
You should pick this up right away.