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Evaluate: int1/(1+3sin^2x)\ dx...

Evaluate: `int1/(1+3sin^2x)\ dx`

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`int1/(1+3sin^2x)\ dx`
`=int frac{sec^2x}{sec^2x+3tan^2x}dx`
`=int frac{sec^2x}{1+4tan^2x}dx`
`x=t` and `sec^2xdx=dt`
`=1/4 int 1/frac{1/4}{t^2}dt `
`=1/4 xx1/2 tan^(-1)t/2+C`
`=1/8 tan^(-1)(tanx/2)+C`
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