emag Integration problem! HELP!

[Bigfoots mum]

Now then, im 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 whats 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

[Dickfore]

First of all, try to find the partial derivative with respect to x (treating z as a constant parameter) of the textbook's answer. If it gives your integrand, then it is correct. If not, it is wrong.

[Bigfoots mum]

Iv used a computer, and it tells me its correct! Otherwise, yes i would have done as you said.

[Dickfore]

So, I guess this issue is resolved.

[Bigfoots mum]

No its not, my question is why is this integral equal to the quoted answer. I gave my attempt at the answer, which is nothing like the actual answer. Im baffled.

[Dickfore]

Oh, so you want to calculate the integral.

Try the substitution x = z \, \tan(p).