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integration of rootsinx

Sorry But this integral is not elementary.We can reduce it to elliptical integral.To see this let u=sinx so, x=arc sinu and dx=du/[1-u^1/2]^1/2And then on rationalising the denominator, ∫ √(u-u³ du/(1-u²)Since you have the square root of a cubic polynomial in the integrand, you now have an elliptic integral. Finally, here is the result from the Wolfram integrator for the original problem:-2E(1/4(π-2x) | 2), where E is an elliptic integral of the second kind.

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integration of rootsinx

I think so 1/2COSx

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