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Evaluate: int(sin^(-1)x)^2\ dx...

Evaluate: `int(sin^(-1)x)^2\ dx`

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` int (sin^(-1)x)^(2) dx`
`= int 0^(2) ,cos 0 d0`
`=0^(2) int cos 0 d0 " "underset(rArr dx = cos 0)(" Let " x=sin 0)`
` -int {(d)/(d0).0^(2),int cos 0 d0 }d0`
` =0^(2) sin0 - int 20 sin 0 d0`
`=0^(2) sin0 - int 2[0 int 0 d0-`
`int {(d)/(d0).0 int sin 0 d0 } d0]`
` =0^(2) sin0 - 2[ -0cos + int cos 0 d0]`
` =0^(2) sin0 + 20 cos 0 -2 sin 0+c`
`=x. (sin^(-1)x)^(2)`
`+2sqrt(1-x^(2)).sin^(-1) x -2x +C`
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