Integral - u substitution with arctan

[walksintoabar]

Homework Statement

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

Homework Equations

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]

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]

$$x=z\sinh t$$

is also a valid substitution.