Integral of Function: Solve Here!

[endoparasite]

hi every one ,
i want to find the integral of function given in the attachment.Please help!

 

[paulfr]

www.wolframalpha.com

 

[Grufey]

try using, \cos 2x=\cos^2x-\sin^2x

and \cos^2x/2=\sqrt{\frac{1+\cos x}{2}}

 

[physeven]

there was another post on this here: https://www.physicsforums.com/showthread.php?t=444905

but to reiterate, it is an elliptic integral. learn what complete elliptic integrals are before you attempt this problem. however, if you do know what elliptic integrals are, you would know that it would be sqrt(2)xE(x|0.5) where E(x) is an elliptic integral of the second kind.