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springo
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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.
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