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(1)/(1-cotx)...

`(1)/(1-cotx)`

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`"Let I"=int (1)/(1-cotx)dx`
`=int (1)/(1-((cos x)/(sinx)))dx`
`=int(sin x)/(sinx -cosx)dx`
`=(1)/(2)int (2sin x)/(sinx-cos x)dx`
`=(1)/(2)int((sin x-cosx)+(cos x+sin))/(sin x-cosx)dx `
`=(1)/(2) int[1+(cos x+sinx)/(sinx-cosx)]d`
`=(1)/(2) int1 dx+(1)/(2)int(cos x+sinx)/(sinx-cosx)dx`
`=(x)/(2)+(1)/(2)log|sin x-cosx|+c`
`.......[because (d)/(dx)(sin x-cos x)=cos x+sin x and int(f'(x))/(f(x))dx=log|f(x)|+c]`
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