$\displaystyle \int \frac {1}{(x^2+a^2)^{3/2}}dx$

$\displaystyle \int \frac {1}{(\sqrt{(x^2+a^2)})^3}dx$

$\displaystyle x=a tan\theta$

$\displaystyle dx=sec^2\theta $

$\displaystyle \sqrt{(x^2+a^2)}= \sqrt{a^2tan^2\theta+a^2}= asec\theta\ ?$

$\displaystyle \int \frac {1}{({asec\theta})^3}sec^2\theta\ ?$