integrate $\int\frac{x\cdot dx}{(x^3+1)^2}$ What methods are there to integrate: $$\int\frac{x\cdot dx}{(x^3+1)^2}$$
I know about partial fractions: 
$$\int\frac{x\cdot dx}{(x^3+1)^2} $$
$$= \int\frac{x\cdot dx}{((x+1)(x^2-x+1))^2} $$
$$= \int \left(\frac{A}{x+1}+\frac{Bx+C}{(x+1)^2} + \frac{Dx+E}{x^2-x+1} + \frac{Fx^3+Gx^2+H+I}{(x^2-x+1)^2}\right)dx$$ and after this solving is easy, i was trying to do the same many times, but i can't find coefficients because mistakes or something other.
I want to know about another methods to solve it.

HINT:
First integrate by parts, 
$$3I=\int\dfrac1x\cdot\dfrac{3x^2}{(1+x^3)^2}dx=-\dfrac1{x(1+x^3)}+\int\dfrac{dx}{x^2(1+x^3)}$$
Now use Partial fraction $$\dfrac1{x^2(1+x^3)}=\dfrac Ax+\dfrac B{x^2}+\dfrac C{x+1}+\dfrac{Dx+E}{x^2-x+1}$$
