Evaluate: `int1/(1-tanx)\ dx`

Explanation

We have given

`int 1/(1-tanx) dx`

`I=int 1/(1-tanx) dx`

`I=int 1/(1-(sinx)/(cosx)) dx`

`I=int 1/((cosx-sinx)/(cosx)) dx`

`I=int (cosx)/(cosx-sinx)dx`

`I=1/2int (2cosx)/(cosx-sinx)dx`

`I=1/2int (cosx+sinx)/(cosx-sinx)dx+1/2intdx`

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