Find $\int \frac {x^2}{x^3+1} dx$. What is my mistake? $\int \frac {x^2}{x^3+1} dx$
$ u = 3x+1, du=3x^2 dx$
$\int \frac{3 du}{u} $
Am I wrong something? Why the answer is $\int \frac{du}{3u}$ instead of $\int \frac{3 du}{u} $ ?
Thank you.

If you set $u=x^3+1$ (so that $du = 3x^2dx$), then $x^2dx = \frac{du}{3}$ and 
$$
\int \frac{x^2 dx}{x^3 +1} = \int \frac{\frac{du}{3}}{u} =\int  \frac{du}{3u}.
$$
