Can a Simple Integral Solve 1/(K + x^2)^(3/2)?

[Mattofix]

A simple integral?!?

Homework Statement

Integrate 1/(K+ x^2)^(3/2) dx

Homework Equations

The Attempt at a Solution

substitution of some kind - if it had an x on top it would be fine...

 

[arildno]

Set $$x=\sqrt{K}Sinh(u)$$ and proceed.

 

[HallsofIvy]

arildno loves that hyperbolic substitution!

Myself, I would have immediately thought that "$tan^2(\theta)+ 1= sec^2(\theta)$" and used the substitution $x= \sqrt{K}tan(\theta)$. I suspect it is just a matter of taste.