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Evaluate: int(x-1)/((x+1)sqrt(x^3+x^2+x)...

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

Text Solution

Verified by Experts

`rArr I=int(x^(2)-1)/((x+1)^(2)sqrt(x^(3)+x^(2)+x))dx` [Muliplying the `N^(')` and `D^(') by (x+1)]`
`I=int(x^(2)-1)/((x^(2)+2x+1)sqrt(x^(3)+x^(2)+x))` dx
`rArr I=int(1/x^(2))/((x^(2)+2x+1)sqrt(x^(3)+x^(2)+x))`dx
`rArr I = int(1-1/x^(2))/(x+1/x+2)(sqrt(x+1/x+1))dx` (Dividing `N^(')` and `D^(')` by `(x+1)]`
`rArr I=2tan^(-1)sqrt(x+1/x+1+C)`
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