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Evaluate: int((x^5-x)^(1/5))/(x^6)\ dx...

Evaluate: `int((x^5-x)^(1/5))/(x^6)\ dx`

Text Solution

Verified by Experts

The correct Answer is:
`(4)/(15)(1-(1)/(x^(3)) )^(5//4)+C`
`int((x^(4)-x)^(1//4))/(x^(5))dx=int(1)/(x^(4))(1-(1)/(x^(3)))^(1//4)dx,`
` "Putting "1-(1)/(x^(3))=t, " we get" `
`I=(1)/(3)int t^(1//4)dt =(4)/(15)t^(5//4)+C=(4)/(15)(1-(1)/(x^(3)) )^(5//4)+C`
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