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Evaluate: int(x^2tan^(-1)x^3)/(1+x^6)dx...

Evaluate: `int(x^2tan^(-1)x^3)/(1+x^6)dx`

Text Solution

Verified by Experts

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