Evaluate: (i) `int(cos2x+2\ sin^2x)/(cos^2x)\ dx` (ii) `int(2\ cos^2x-cos2x)/(sin^2x)\ dx`

Explanation

evaluate `\int \frac{\cos 2 x+2 \sin ^{2} x}{\sin ^{2} x} d x`


\text { let } I `=\int \frac{\cos 2 x+2 \sin ^{2} x}{\sin ^{2} x} d x `


`=\int \frac{(2 \cos ^{2} x-1)+2 \sin ^{2} x}{\sin ^{2} x} d x `


`=\int 2 \frac{.\cos ^{2} x+\sin ^{2} x)-1}{\sin ^{2} x} d x`


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