Evaluate $\int_0^\infty\frac{dl}{(r^2+l^2)^{\frac32}}$ How to evaluate the following integral
$$\int_0^\infty\frac{dl}{(r^2+l^2)^{\large\frac32}}$$
The solution is supposed to look like this, unfortunately I can't derive it.
$$
\left[\frac{l}{r^2\sqrt{r^2+l^2}}\right]_{l=0}^\infty
$$

All integrals of the form $\displaystyle\int_0^\infty\frac{x^{k-1}}{(x^n+a^n)^m}dx$ can be expressed in terms of trigonometric functions 
as follows: first, let $x=at$, then $u=\dfrac1{t^n+1}$. Now recognize the expression of the beta function in 
the new integral, and finally use Euler's reflection formula for the $\Gamma$ function in order to arrive at 
the desired result.
