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Question

Evaluate the following :
cosec3xdx

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Solution

I=cosec3dx
= Integration by part
cosec=u;v=cosec2x
dudx=coseccotx;vdx=cotx
(cosecx)cotxcot2xcosecdx=I
(cosecx)cotx(cosec2x1)cosecxdx=I
I=cosecxcotxcosec3xdx+cosecxdx
2I=cosecxcotx+cosecxdx
I=cosecxcotx2+12cosecxdx
I=cosecxcotx2+12ln|cosecxcotx|+c

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