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Evaluate: int(dx)/(x^(2/3)(1+x^(2/3)))...

Evaluate: `int(dx)/(x^(2/3)(1+x^(2/3)))`

Text Solution

Verified by Experts

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