Question

Integrate x/(x^2+y^2)^(3/2) dx.

Answer 1

@aaronq @Loser66

Answer 2

\[\int \dfrac{x}{\sqrt{(x^2+y^2)^3}}dx\\=\int\dfrac{x}{(x^2+y^2)\sqrt{x^2+y^2}}dx\]
Let \(u=\sqrt{x^2+y^2}\) \(u^2= x^2+y^2\) and du =\(\dfrac{x}{\sqrt{x^2+y^2}}dx\)
Plug all in
\[\int \dfrac{du}{u^2}= \int u^{-2}du\]
I think you can handle it from here.