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

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

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`I=int frac{(x^{2}+x+1)}{(x+1)^{2}(x+2)} d x `
`text { Let } frac{x^{2}+x+1}{(x+1)^{2}(x+2)}=frac{A}{x+1}+frac{B}{(x+1)^{2}}+frac{C}{x+2} `
`Rightarrow frac{x^{2}+x+1}{(x+1)^{2}(x+2)}=frac{A(x+1)(x+2)+B(x+2)+C(x+1)^{2}}{(x+1)^{2}(x+2)} `
`Rightarrow x^{2}+x+1=A(x^{2}+x+2 x+2)+B x+2 B+C(x^{2}+2 x+1) `
`Rightarrow x^{2}+x+1=(A+C) x^{2}+(3 A+B+2 C) x+(2 A+2 B+C) `
`text { Equating coefficient of like terms. } `
`A+C=1 ldots ldots(1) `
`3 A+B+2 C=1 ldots ldots(2) `
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