Question

Integrate $\frac{x^2+5x+5}{x^2+3x+2}$ with respect to $x$.

Answer 1

$I=\int \frac{x^2+3x+2}{x^2+3x+2}+\frac{2x+3}{x^2+3x+2}dx$

$=\int 1+\frac{f^{\prime }\left(x\right)}{f\left(x\right)}dx\left(f\right(x)=x^2+3x+2)$

$=x+log(x^2+3x+2)+c$