- #1

CalcYouLater

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## Homework Statement

Perform the following integration:

[tex]\int_{0}^{\sqrt{2}h}\frac{x}{\sqrt{h^2+x^2-\sqrt{2}hx}}dx[/tex]

## Homework Equations

The solution (via wolframalpha.com) is:

[tex][\sqrt{h^2+x^2-\sqrt{2}hx}+\frac{h}{\sqrt{2}}ln(2(\sqrt{h^2+x^2-\sqrt{2}hx}+x)-\sqrt{2}h)[/tex]

Evaluated from 0 to sqrt(2)h

Here is the link: http://www.wolframalpha.com/input/?i=x/[(h^2+x^2-(2^(1/2))*x*h)^(1/2)]

## The Attempt at a Solution

I immediately looked at a substitution and an integration by parts. They left me worse off than before. Then, I went to wolframalpha in order to see how to do it. They could not show any steps. I am not sure how to integrate this by hand. Any advice?

If this is an integral that you simply look up in a table, could someone point me to the methods used (no matter how complex) that will solve this?

Thanks for reading.