$\displaystyle \int \frac{x^3}{(x^2+5)^2} dx

$

$\displaystyle

u=x^2

$

$\displaystyle

du = 2xdx.\frac{x^2}{x^2}

$

$\displaystyle

\frac{udu}{2}=x^3dx

$

$\displaystyle \frac{1}{2}\int \frac {udu}{(u+5)^2}$

$\displaystyle \frac{1}{2}[\int \frac {du}{u+5} - \int \frac{5du}{(u+5)^2}]$

$\displaystyle \frac{1}{2}[ln(u+5) +\frac{5}{(u+5)}]$

$\displaystyle \frac{1}{2}[ln(x^2+5) +\frac{5}{(x^2+5)}]$

But the answer is different.

Please help me finding which step is wrong.