I forgot how to do this integration Help

[Karmerlo]

Homework Statement

Do the integration

Homework Equations

The Attempt at a Solution

I forgot how to do this integration with another method. I think I can do it through Trigonometric Method. But I remember that there is still another way to do it without using Trigonometric Method. Anyone can show me steps to do it? Thanks.

 

[Clever-Name]

Well, for the trig method you would use the substitution let x = ytan(u)
If that gets you the right answer then why bother with another method. I can't think of a different method right now that would work.

 

[SammyS]

Take the derivative of \displaystyle \frac{x}{y^2\sqrt{x^2+y^2}}\,, treating y as a constant, of course. Then see if you can reverse the process.

 

[dextercioby]

Try a substitution x=y \sinh t. The resulting integration will be trivial.