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int(x-sinx)/(1-cosx)dx...

`int(x-sinx)/(1-cosx)dx`

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we have given,
`int(x-sinx)/(1-cosx)dx`
`I=int(x−sinx)/(1−(1−2sin^2(x/2)))dx`
`=int(x−sinx)/(2sin^2(x/2))dx`
`=1/2int(x)/(sin^2(x/2))−1/2int(2sin(x/2)cos(x/2))/(sin^2(x/2))dx`
`=1/2intx.cosec^2(x/2)−intcot(x/2)dx`
`=1/2[x.intcosec^2(x/2)−int{d/(dx)x.intcosec^2(x/2)dx}dx]−ln∣2sin(x/2)∣`
`=1/2[−x.2cot(x/2)+int1.cot(x/2).2dx]−ln∣2sin(x/2)∣`
`=1/2[−2xcot(x/2)+2ln∣sin(x/2).2∣]`
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