Evaluate: `int1/(sqrt(1+sin2x))\ dx`

Explanation

`\text { evaluate: } \int \frac{1}{\sqrt{1+\sin 2 x}} d x`


`I=\int \frac{1}{\sqrt{1+\sin 2 x}} d x`


`\sin 2 x=\frac{2 \tan x}{1+\tan ^{2} x} \quad ; \quad \sec ^{2} x-\tan ^{2} x=1`


`I=\int \frac{1}{1+\frac{2 \tan x}{1+\tan ^{2} x}} d x=\int \frac{1}{1+\frac{\tan ^{2} x+2 \tan x}{\sec ^{2} x}} d x`


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