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Evaluate intx^3(x^(4)+1)^(-1)dx...

Evaluate `intx^3(x^(4)+1)^(-1)dx`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(4) log(x^(4)+1)+C`
`inte^(3logx)(x^(4)+1)^(-1)dx=inte^(logx^(3))(dx)/(x^(4)+1)=int(x^(3)dx)/(x^(4)+1)`
`=(1)/(4)int(4x^(3))/(x^(4)+1)dx`
`=(1)/(4) log(x^(4)+1)+C`
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