[tex]\int \frac{x}{\left(x^2+z^2\right)^{3/2}} \, dx[/tex]

[eschiesser]

Homework Statement

$$\int \frac{1}{\left(x^2+z^2\right)^{3/2}} \, dx$$

I have been trying various u-substitutions for about 2 hours now, but I cannot seem to find a way to solve this by hand! I used mathematica to solve the problem. I feel like it will be fairly straightforward once I figure out what u should be, if u-sub is the way to go.

This is for my electrodynamics course, and getting hung up on integrals is not helpful.

I've tried:
u=x^2
u=1/(x²+z²)^1/2
u=1/(x²+z²)
u=1/(x²+z²)^3/2
u=x/(x²+z²)^1/2
u=x/(x²+z²)
u=(x²+z²)^1/2
u=(x²+z²)
u=(x²+z²)^3/2

 

[gabbagabbahey]

Have you tried a trig substitution...something like $x=z\tan\theta$ looks appropriate

 

[eschiesser]

wow...never even crossed my mind to use trig substitution. In fact, I completely forgot that as a method. And its so useful! Thank you! I guess I ought to review calc 2 stuff from HS...

Thanks again!