Evaluate:
(i) `int(cosx)/(1-cosx)\ dx`
(ii) `int(cos^2x-sin^2x)/(sqrt(1+cos4x))\ dx`

Explanation

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


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


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


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


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


`=-x-cotx-cosecx+C`



(ii) `int(cos^2x-sin^2x)/(sqrt(1+cos4x))\ dx`


`=(1)/(sqrt(2))int (cos2x)/(cos2x)\dx`


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