∫cos⁵x√sinxdx

Hi Suhas,

MAke the sub sinx = t^2, so that cosxdx = 2tdt.

And cos^4x = (1-sin^2 x)^2 = (1-t^4)^2

So that the integral becomes ∫[(1-t^4)^2]2t^2dt.

Open the brackets. Directly integrable.

Hope it helps.

Best Regards,

Ashwin (IIT MadraS).