Question

Evaluate:
$\int \frac{x^2+5x+2}{x+2}dx$

Answer 1

$\begin{array}{c}\int \frac{x^2+5x+2}{x+2}dx\\ \Rightarrow \int \frac{x^2+4x+x+2}{x+2}dx\\ \Rightarrow \int \frac{x^2+4x+4-4}{x+2}dx+\int \frac{x+2}{x+2}dx\\ \Rightarrow \int \frac{{\left(x+2\right)}^2}{x+2}dx-\int \frac{-4}{x+2}dx+x\\ \Rightarrow \frac{x^2}{2}+2x-4\log (x+2)+x+C\\ \Rightarrow \frac{x^2}{2}+3x-4\log (x+2)+C\end{array}$

Hence, this is the answer.