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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:
`-((x^(4)+1)^(1//4))/(x)+c`
Let `I=int (dx)/(x^(2)(x^(4)+1)^(3//4))=int(dx)/(x^(2)*x^(3)(1+(1)/(x^(4)))^(3//4))`
Put `1+x^*(-4)=t rArr -(4)/(x^(5))dx = dt`
`therefore" "I=-(1)/(4)int(dt)/(t^(3//4))=-(1)/(4)*(t^(1//4))/(1//4)+c=-(1+(1)/(x^(4)))^(1//4)+c`
`=-((x^(4)+1)^(1//4))/(x)+c`
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