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Evaluate the definite integrals int2 ...

Evaluate the definite integrals `int2 3(dx)/(x^2-1)`

Text Solution

Verified by Experts

`int_(2)^(3)(1)/(x^(2)-1)dx=[(1)/(2)log|(x-1)/(x+1)|]_(2)^(3)`
`=(1)/(2)log |(3-1)/(3+1)|-(1)/(2)log|(2-1)/(2+1)|`
`=(1)/(2)log|(2)/(4)|-(1)/(2)log |(1)/(3)|`
`=(1)/(2)[log(1)-log(2)`
`-log (1)+log (3)]`
`=(1)/(2)log ((3)/(2))`
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