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Evaluate: int(x^3)/(sqrt(1-x^8))dx...

Evaluate: `int(x^3)/(sqrt(1-x^8))dx`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(3)"sin"^(-1)(x^(3))+C`
`I=int(x^(2))/(sqrt(1-x^(6)))dx=int(x^(2))/(sqrt(1^(2)-(x^(3))^(2)))dx`
` "Let "x^(3)dx=dt`
` :. I=(1)/(3)int(dt)/(sqrt(1-t^(2)))=(1)/(3)"sin"^(-1)(t)+C=(1)/(3)"sin"^(-1)(x^(3))+C`
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