# Integral - u substitution with arctan

## Homework Statement

integral of 1/(x^2 + z^2)^(3/2) dx,
where z is a constant

## The Attempt at a Solution

I set u = arctan(x/z) so du = z/(x^2 + z^2) dx but now I'm honestly stuck.

Dick
Homework Helper
You've got the correct substitution but you are thinking of this in a kind of convoluted way. Just put x=z*tan(u), so dx=z*sec(u)^2*du. Factor out a power of z and do the trig integral in u.

dextercioby
$$x=z\sinh t$$