- #1

- 126

- 0

## Homework Statement

Find:

[tex]\int_{0}^\infty \frac{\sqrt[3]{x}-\sqrt{x}}{x^b+a^b}dx[/tex]

With x>0 and a>2.

## Homework Equations

## The Attempt at a Solution

I think it's probably something with Beta, but I'm not sure how to change it into the proper form.

I thought changing it into:

[tex]\int_{0}^\infty \frac{\sqrt[3]{x}-\sqrt{x}}{x^b\left(1+\left(\frac{a}{x}\right)^b\right)}dx[/tex]

And then doing:

[tex]\tan^2 t = \left(\frac{a}{x}\right)^b[/tex]

But it makes things too complicated, so I guess it's not the way to go.

Thanks for your help.

Last edited: