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Evaluate: intsin^(-1)x\ dx...

Evaluate: `intsin^(-1)x\ dx`

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We have given `intsin^(-1)x\ dx`
`I=intsin^(-1)x\ dx`
Let `u=sin^(-1)x`,`dv=dx`
`implies du=1/(sqrt(1-x^2))dx`,`v=x`
`I=intsin^(-1)x\ dx=xsin^(-1)x-int(x)/(sqrt(1-x^2))dx+c....(1)`
Let `w=1−x^2`
`implies xdx=-(dw)/2`
`I=xsin^(-1)x+int(dw)/(2sqrtw)`
...
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