Can a substitution solve this integral problem with Emag integration?

[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

 

[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. I am baffled.

 

[Dickfore]

Oh, so you want to calculate the integral.

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