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Evaluate: int1/([(x-1)^3(x+2)^5]^(1/4))d...

Evaluate: `int1/([(x-1)^3(x+2)^5]^(1/4))dx`

Text Solution

Verified by Experts

`I=int(1)/(((x-1)/(x+2))^(3//4)(x+2)^(2))dx`
Let `(x-1)/(x+2)=t " or " (3dx)/((x+2)^(2))=dt`
` :. I=(1)/(3)int(1)/(t^(3//4))dt=(1)/(3)((t^(1//4))/(1//4))+C`
`=(4)/(3)t^(1//4)+C=(4)/(3)((x-1)/(x+2))^(1//4)+C`
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