Fairly basic integral failing to become solved. O:-)

[Saraphim]

"Fairly" basic integral failing to become solved. O:-)

Hi,

I'm having trouble with an integral where I simply do not know where to start. I just need a little nudge in the right direction. I've tried integration by parts and by substitution, but I'm really just stumbling in the dark and should obviously choose something in a more well-informed manner. If I could just get a nudge in the right direction I think that I can solve it. :)

Homework Statement

$$\int (x^2+z^2)^{-3/2}dx$$

 

[ChaoticLlama]

when you see a square root in your integrand, you will likely want to attempt trig substitution if there is no other obvious route.

There are 3 different trig substitutions possible based on the form under the root:

x = z * sin@
x = z * tan@
x = z * sec@

you should know which one to use based on that form.

tell us which is the correct substitution, and you should be able to solve it.

 

[Saraphim]

I'll have a go at that, thank you very much.

 

[Mark44]

Try a trig substitution, tan u = x/z. Keep in mind that z^2 is a constant in this integral.