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

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

Text Solution

Verified by Experts

The correct Answer is:
`log|(x^(2)-1)/(x)|+C`
`int(x^(2)+1)/(x(x^(2)-1))dx=int(x^(2)+1)/(x(x-1)(x+1))dx`
`=int((-1)/(x)+(1)/(x-1)+(1)/(x+1))dx`
`=log|x-1|+log|x+1|-log|x|+C`
`=log|(x^(2)-1)/(x)|+C`
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