Solving Bizarre Integral: x/[z2(x2+z2)1/2]

[Bigfoots mum]

Now then, I am close to shedding a tear with this one.

This integral has been popping up in a few electromag examples iv been doing and i have absolutely no idea what's going on here.

The integral is 1/[(x²+z²)^3/2] with respect to x

According to the textbook the answer is x/[z²(x²+z²)^1/2]

I initially, without evening really thinking, went straight for -1/(x[x²+z²]^1/2)

Any ideas?
Thanks

 

[Cyosis]

Use the substitution $x=z \tan u$.

 

[annoymage]

btw, you left a constant