Integration Problem: Solving Compact Results in Electrodynamics

[Psi-String]

Hi! Could someone give me an idea how the following integration be carried out??

\int \frac{r dr}{ \left( r^2 + a^2 - 2rau \right)^{3/2}} = \frac{ru - a}{a(1-u^2)\sqrt{r^2 + a^2 - 2rau}}

where u and a are constant.

I have encounter such integration several times in electrodynamics.

I can solve it in lengthy way, but can't carry out such compact result as above. Could someone help me?? Thanks a lot!

 

[unplebeian]

Look up Sadikus textbook. Or David Griffiths. You'll find a good result there.

 

[Psi-String]

well, this is an integration I need to carry out when solving Griffiths' problem. The solution manual only give the result as above, it didn't take out step by step, and I don't think it is that obvious that we can solve it just by one equation XDDDD