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Question

Integrate sin2x1-cosxdx.


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Solution

Compute the given integration.

In the question, an integration sin2x1-cosxdx is given.

Assume that, I=sin2x1-cosxdx.

I=sin2x1-cosxdxsin2x+cos2x=1I=1-cos2x1-cosxdx1-cos2x=1-cosx1+cosxI=1+cosxdxI=dx+cosxdxcosxdx=sinx,dx=xI=x+sinx+C

Hence sin2x1-cosxdx=x+sinx+C.


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