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Evaluate: int1/((1+x^2)sqrt(1-x^2))dx...

Evaluate: `int1/((1+x^2)sqrt(1-x^2))dx`

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`int1/((1+x^2)sqrt(1-x^2))dx`
Put `x=sinθ`
`∴I=∫(cosθdθ)/((1+sin^2θ)(cosθ))`
`=∫(dθ)/(1+sin^2θ)`
`=∫(cosec^2θdθ)/(2+cot^2θ)`
Put `cotθ=t`
`∴−cosec^2θdθ=dt`
...
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