Originally Posted by

**albi** You cannot do that:

$\displaystyle

\int (u)^2\: \frac{du}{2x}\:\:\Rightarrow \:\:\frac{1}{2x}\:\int (u)^2\:du\:\:= \:\:\frac{1}{2x}\:\times\frac{(u)^3}{3}\:

$

You should not treat x as a constat, because it depends on u. The only way to do that would be to express x in a terms of u. You can do that solving the equation for x:

$\displaystyle x^2 - (u+1) = 0$ since u+1 >0 we get

$\displaystyle x = \pm \sqrt{u+1}$

Hence the integral is

$\displaystyle

\frac{1}{2}\int u^2\: \frac{du}{\pm \sqrt{u+1}}$

Good luck.