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Evaluate: int(1/((x+1)^(1/3)+sqrt(x+1)))...

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

Text Solution

Verified by Experts

Given
`int(1/((x+1)^(1/3)+sqrt(x+1)))dx`
`I=int(1/((x+1)^(1/3)+sqrt(x+1)))dx`
Let `(x+1)=l^6`
`implies dx=6l^5dl`
Then
`I=int(1/((l)^(6\times(1/3))+(l)^(6\times(1/2)))6l^5dl`
`I=int(6l^5dl)/(l^2+l^3)`
...
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