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

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

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The correct Answer is:
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Let `I int(sin^(-1)x)/((1-x^(2))^(3//4))dx = int(sin^(-1)x)/((1-x^(2))sqrt(1-x^(2)))dx`
Put `sin^(-1)x =t rArr (1)/(sqrt(1-x^(2)))dx = dt`
and `x sint rArr 1 - x^(2) = cos^(2)t`
`rArr cost = sqrt(1-x^(2))`
`:. I = int(t)/(cos^(2)t) dt = intt. sec^(2)tdt`
`= t.intsec^(2)tdt - int(d/(dt)t. intsec^(2)tdt)dt`
`= t.tant - int1. tan tdt`
` = t tan t + log|cost|+C , [:' int tan xdx = -log|cosx|+C]`
`sin^(-1)x.(x)/(sqrt(1-x^(2))) + log|sqrt(1-x^(2))|+C`
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