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

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

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Given:`intsin^(- 1)sqrt(x/(a+x))dx`
`I=intsin^(- 1)sqrt(x/(a+x))dx`
Let `x=atan^2t implies dx=2atantsec^2tdt`
`I=intsin^(- 1)sqrt((atan^2t)/(a+atan^2t))2atantsec^2tdt`
`I=2a int sin^(–1) (sin t) tan t sec^2t dt`
`I= 2a int t tan t sec^2t dt`
Let `tan t = u`
`= sec^2 t dt = du`
...
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