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

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

Text Solution

Verified by Experts

The correct Answer is:
`x-(sin^(-1)x)sqrt(1-x^(2))+C`
` "Putting " sin^(-1)x=t " and " (1)/(sqrt(1-x^(2)))dx=dt, " we get " `
` int(xsin^(-1)x)/(sqrt(1-x^(2)))dx=int tsin t dt=-t cost+sin t+C`
`=-sin^(-1)xcos(sin^(-1)x)+sin(sin^(-1)x)+C`
`=x-(sin^(-1)x)sqrt(1-x^(2))+C`
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