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Evaluate: int5/((x^2+1)(x+2))\ dx...

Evaluate: `int5/((x^2+1)(x+2))\ dx`

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`I=int frac{5 d x}{(x^{2}+1)(x+2)} `
`text { Let } frac{5}{(x+2)(x^{2}+1)}=frac{A}{x+2}+frac{B x+C}{x^{2}+1} `
`Rightarrow frac{5}{(x+2)(x^{2}+1)}=frac{A(x^{2}+1)+(B x+C)(x+2)}{(x+2)(x^{2}+1)} `
`Rightarrow 5=A(x^{2}+1)+B x^{2}+2 B x+C x+2 C `
`Rightarrow 5=(A+B) x^{2}+(2 B+C) x+(A+2 C)`
Equating coefficients of like terms
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