Evaluate: (i) `int1/(sqrt(1+cos2x))\ dx` (ii) `int1/(sqrt(1-cosx))\ dx`

Explanation

`\text { calculate i) } \int \frac{1}{1+\cos x x} d x`


`I=\int \frac{1}{\sqrt{1+\cos 2 x}} d x \Rightarrow I=\int \frac{1}{\sqrt{2 \cos ^{2} x}} d x`


`I=\int \frac{1}{\sqrt{2} \cos \frac{x}{2}} d x=\frac{1}{\sqrt{2}} \int \sec \frac{x}{\frac{1}{2}} d x`


`I=\frac{1}{\sqrt{2}} \cdot \ln |\sec \frac{x}{2}+\tan \frac{x}{}|+c`


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