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

Explanation

`int (x-sinx)/(1-cosx)dx`
`=int (x)/(1-cosx)dx-int (sinx)/(1-cosx)dx`
`=(1)/(2)int x "cosec"^(2)(x)/(2)dx-int (2sin x//2 cos x//2)/(2sin^(2)x//2)dx`
`=(1)/(2)int underset (I)(x)underset(II)("cosec"^(2))(x)/(2) dx-int"cot"(x)/(2) dx`
`=(1)/(2){x(-2"cot"(x)/(2))-int1 *(-2 "cot"(x)/(2))dx}-int "cot"(x)/(2)dx +c`
`= -x"cot"(x)/(2)+int "cot"(x)/(2)dx-int "cot"(x)/(2)dx+c`
`= -x "cot"(x)/(2)+c.`