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

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

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