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

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

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`I=int frac{(2 x+1) d x}{(x+2)(x-3)^{2}}`
`text { Let } frac{2 x+1}{(x+2)(x-3)^{2}}=frac{A}{x+2}+frac{B}{x-3}+frac{C}{(x-3)^{2}}`
`Rightarrow frac{2 x+1}{(x+2)(x-3)^{2}}=frac{A(x-3)^{2}+B(x+2)(x-3)+C(x+2)}{(x+2)(x-3)^{2}}`
`Rightarrow 2 x+1=A(x^{2}-6 x+9)+B(x^{2}-x-6)+C(x+2)`
`Rightarrow 2 x+1=(A+B) x^{2}+(-6 A-B+C) x+(9 A-6 B+2 C)`
`text { Equating the coefficients of like terms }`
`A+B=0 ldots ldots ldots ldots . ldots .(1)`
`-6 A-B+C=2 ldots ldots ldots ldots ldots ldots ldots(2)`
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