Evaluate:
(i) `int(1-cosx)/(1+cosx)\ dx`
(ii) `int{3sinx-4cosx+5/(cos^2x)-6/(sin^2x)+tan^2x-cot^2x}\ dx`

Explanation

(i) `int(1-cosx)/(1+cosx)\ dx`


`=int(1+cos^2x-2cosx)/(1-cos^2x)\dx`


`=int(1+cos^2x-2cosx)/(sin^2x)\dx`


`=int(cosec^2x+cot^2x-2cotxcosecx)\dx`


`=int(cosec^2x+cosec^2x-1-2cotxcosecx)\dx`


`=-2cotx-x+cosecx+C`



(ii) `int{3sinx-4cosx+5/(cos^2x)-6/(sin^2x)+tan^2x-cot^2x}\ dx`


`=int{3sinx-4cosx+5sec^2x-6cosec^2x+sec^2x-1-cosec^2x+1}\ dx`


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