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Evaluate: int1/(cos2x+3sin^2x)\ dx...

Evaluate: `int1/(cos2x+3sin^2x)\ dx`

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`int1/(cos2x+3sin^2x)\ dx`
`=int frac{1}{1-2sin^2x+3sin^2x}dx`
`=int 1/(1+sin^2x)dx`
`int frac{sec^2x}{sec^2x+tan^2x}dx`
Let `sec^2x=1+_tan^2x`
`=int {sec^2x}{1+2tan^2x}dx`
`x=t` and `sec^2x=dt`
`=int dt/(1+2t^2)` ...
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