$$\int\limits_{0}^{1} ({{1-x^2 \over 1+x^2}})^{1/2} dx$$

Question

anonymous · Answer

really?  no chance that this is an elementary integral

unklerhaukus · Answer

well im supposed to evaluate it in terms of the gamma function

anonymous · Answer

by which i mean i don't think you can find an "anti- derivative" as an elementary function

unklerhaukus · Answer

the answer has gamma functions in it 
and im guessing these come from beta functions

unklerhaukus · Answer

i just cannot find the correct substitution to get the integral into the form of a Beta function

agreene · Answer

you can use trig sub to get to ellipitcial integrals of the 1st and 2nd... http://en.wikipedia.org/wiki/Elliptic_integral#Incomplete_elliptic_integral_of_the_first_kind Don't really see any other way of doing this--and it's a pain no matter which way you choose.