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

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

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`int frac{(x^{2}+1)}{x(x^{2}-1)} d x`
`=int frac{(x^{2}+1)}{x(x-1)(x+1)} d x`
`text { Let } frac{x^{2}+1}{x(x-1)(x+1)}=frac{A}{x}+frac{B}{x-1}+frac{C}{x+1}`
`Rightarrow frac{x^{2}+1}{x(x-1)(x+1)}=frac{A(x-1)(x+1)+B(x)(x+1)+C(x)(x-1)}{x(x-1)(x+1)}`
`Rightarrow x^{2}+1=A(x-1)(x+1)+B(x)(x+1)+C(x)(x-1) text {. }`
`text { Putting } x-1=0 text { or } x=1 text { in eq. (1) }`
`Rightarrow 1+1=A times 0+B(1)(1+1)+C times 0`
`Rightarrow B=1`
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