In electromagnetic theory, the magnetic potential $u$ at a point on the axis of a circular coil is given by $$u = Ar \displaystyle\int_{a}^{\infty} \frac{\hbox{d}x}{(r^2+x^2)^{(3/2)}}$$ where $A, r, a$ are constants. Compute

$u$ = .

Hint: The integration is a little tricky. Substitute $x = r \tan{\theta}$.