Help with Integral: "Integrating by Parts

[Saladsamurai]

I am trying to work out the integral that takes the form:

$$I=\int \frac{x\, dx}{(a^2+x^2)^{3/2}}$$

I cannot find it in a table, so I am trying By Parts.

Letting $dv=x\,dx$ and letting $u=(a^2+x^2)^{-3/2}$

proves to be futile since I just wind up with a similar integral again, it turns into a vicious cycle

Letting $u=x$ and $(a^2+x^2)^{-3/2}\, dx$ again leaves me with another integral that is not in a table, that is, I get

$$I=\frac{x^2}{a^2\sqrt{a^2+x^2}}-\int\frac{x\, dx}{a^2\sqrt{a^2+x^2}}$$

Is there a better way? Or should I Integrate by Parts again?

This is annoying. It is just an "intermediate step" in a Griffiths E&M problem.

 

[Dick]

It might not be in the table because it's so simple. Just substitute u=(a^2+x^2).

 

[Saladsamurai]

It might not be in the table because it's so simple. Just substitute u=(a^2+x^2).

Well. Aren't you a smarty-pants.

Cannot believe I missed that.

Where is that :commits Sepuku: emoticon?


Oh... and thanks!

 

[Saladsamurai]

Hey T-T I like Dick's u-substitution. It's really quick.

I have actually never used a trig substitution. I will probably post back here in a while as I would like to learn.

For now, I am finishing up my E&M.

Thanks!