Evaluate`intsin^-1sqrt(x/(a+x))dx`

Explanation

`int sin ^{-1}(sqrt{frac{x}{a+x}}) d x`
`
Put x=a tan ^{2} theta`
`
=d x=2 a tan theta sec ^{2} theta d theta`
`
=int sin ^{-1}(sqrt{frac{a tan ^{2} theta}{a+a tan ^{2} theta}}) 2 a tan theta sec ^{2} theta d theta`
`
=2 a int sin ^{-1}(sin theta) tan theta sec ^{2} theta d theta`
`
=2 a int theta tan theta sec ^{2} theta d theta`

Let `tan theta=t`
`
=sec ^{2} theta d theta=d t`
`
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