Evaluate: `int2/(2+sin2x)dx`

Explanation

`int2/(2+sin2x)dx`

`=int frac{2}{2+2sinxcosx}dx`

Divide by `cos^2x`

`=int frac{frac{1}{cos^2x}}{frac{1}{cos^2x}+frac{sinx cosx}{cos^2x}}dx`

`=int frac{sec^2x}{sec^2x-tanx dx}`

`=int frac{sec^2x }{1+tan^2x+tanx}dx`

`tanx=t` and `sec^2xdx=dt`

`=int frac{1}{1+t^2+t}dt`
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