integration of (x+sinx)/(1+cosx)
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Integ.(x-sinx)dx/(1-cosx)
=Integ(x-2sin x/2.cos x/2)dx/2sin^2 x/2
= Integ.{(1/2)x.cosec^2 x/2} - {cot x/2} dx
=Integ.(1/2)x d(-2cot x/2) - integ.cot x/2. dx
=(1/2){-2x cot x/2 +integ.2 cot x/2 .dx} -2logsinx/2 . (using the formula integ.udv = uv - integ.vdu)
=-xcot x/2 -2logsinx x/2–2logsin x/2 + c
=-x.cot x/2–4 log sin x/2 + c
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