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Evaluate: int(dx)/(x^2(x^4+1)^(3/4))...

Evaluate: `int(dx)/(x^2(x^4+1)^(3/4))`

Text Solution

Verified by Experts

The correct Answer is:
`-(1+(1)/(x^(4)))^(1//4)+C`
`int(1)/(x^(2)(x^(4)+1)^(3//4))dx=int (1)/(x^(5)(1+(1)/(x^(4)))^(3//4))dx`
`= -(1)/(4)int(1)/(t^(3//4))dt " where "t=1+(1)/(x^(4))`
`= -(1)/(4)(t^(1//4))/(1//4)+C= -t^(1//4)+C`
` = -(1+(1)/(x^(4)))^(1//4)+C`
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