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#### skatenerd

##### Active member

- Oct 3, 2012

- 114

$$\int_{-1}^{1}\int_{-\sqrt{1-y^2}}^{\sqrt{1-y^2}}\frac{2}{1+y^2}\,dx\,dy$$

and I got it down to

$$\int_{-1}^{1}\frac{4\sqrt{1-y^2}}{1+y^2}\,dy$$

I tried thinking of numerous substitutions and by parts strategies...nothing seemed to work. I consulted wolframalpha and it gave me a solution using I think something like 4 substitutions and partial fractions which I would really rather not go through.

Any other ideas? Or is this just a terrible integral one would prefer to avoid?