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

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

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Let `I=(x^3+x+1)/(x^2-1)`
=`x+(2x+1)/(x^2-1)`
`(2x+1)/(x^2-1)=a/(x+1)+b/(x-1)`
`2x+1=A(x−1)+B(x+1) ........ (1)`
Substituting x=1 and −1 in equation (1), we obtain
A=`1/2`​ and B=`3/2`
`​(x^3+x+1)/(x^2-1)=x+1/(2(x+1))​+3/(2(x−1))`
​ ...
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