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Evaluate: int((x-x^3)^(1/3))/(x^4)dx...

Evaluate: `int((x-x^3)^(1/3))/(x^4)dx`

Text Solution

Verified by Experts

The correct Answer is:
` -(3)/(8)((1)/(x^(2))-1)^(4//3)+C`
`I=int((x-x^(3))^(1//3))/(x^(4))dx=int(((1)/(x^(2))-1)^(1//3))/(x^(3))dx`
` "Putting " (1)/(x^(2))=t, (1)/(x^(3))dx= -(dt)/(2), " we get" `
`I= -(1)/(2)int t^(1//3)dt= -(3)/(8)t^(4//3)+C= -(3)/(8)((1)/(x^(2))-1)^(4//3)+C`
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