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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`

Text Solution

Verified by Experts

`I=int frac{(x^{2}+x-1) d x}{(x+1)^{2}(x+2)}`
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+1)}=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}+3 x+2)+B(x+2)+C(x^{2}+2 x+1)`
Equating coefficients of like terms
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