Originally Posted by

**Lites** I need help to integrate this particular integral step-by-step. I've been wrestling around with substitution method without any satisfying result. I don't know I'm doing wrong with it.

$\displaystyle \int_{-a}^a \frac{1}{\left(x^2+y^2\right)^{3/2}} \, dy$

This is my attempt:

Let u = $\displaystyle \left(x^2+y^2\right)$

du = $\displaystyle 2y\text{dy}$

Hence:

$\displaystyle \int \frac{1}{\left(x^2+y^2\right)^{3/2}} \, dy

\int \frac{u^{-3/2}}{2} \, du

\frac{1}{2} \int u^{-3/2} \, du

\frac{\frac{1}{\sqrt{u}}}{\frac{2 (-1)}{2}}-\frac{1}{\sqrt{u}}-\frac{1}{\sqrt{x^2+y^2}}-\frac{1}{\sqrt{x^2+y^2}}$

$\displaystyle -\frac{1}{\sqrt{x^2+y^2}}$

Thank You