Question

integration of (x+sinx)/(1+cosx)​

Answer 1

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