Question

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

Answer 1

really? no chance that this is an elementary integral

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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.