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int(xsin^(- 1)x)/((1-x^2)^(3/2)) dx...

`int(xsin^(- 1)x)/((1-x^2)^(3/2)) dx`

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Given:`int(xsin^(- 1)x)/((1-x^2)^(3/2)) dx`
`I=int(xsin^(- 1)x)/((1-x^2)^(3/2)) dx`
`I=int(xsin^(- 1)x)/((1-x^2)^(1/2)(1-x^2)) dx`
Let `sin^(−1)x=t`
`implies (dx)/((1-x^2)^(1/2))=dt`
`I=int (sin t .t )/(1-sin^2t)dt`
`I=int (sin t .t )/(cos^2t)dt`
`I=int ttantsectdt`
...
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