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Evaluate: int(dx)/(x^2(1+x^5)^(4/5))...

Evaluate: `int(dx)/(x^2(1+x^5)^(4/5))`

Text Solution

Verified by Experts

The correct Answer is:
` -((1+x^(5))^(1//5))/(x)+C`
`I=int(dx)/(x^(2)(1+x^(5))^(4//5))=int(dx)/(x^(6)((1)/(x^(5))+1)^(4//5))`
` "Let " t=1+(1)/(x^(5)) " or " dt= -(5dx)/(x^(6))`
` :. I= -(1)/(5) int(dt)/(t^(4//5))= -t^(1//5)+C= -(1+(1)/(x^(5)))^(1//5)+C`
`= -((1+x^(5))^(1//5))/(x)+C`
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