Question

∫(x^2 - x + 2)dx

Explanation:

Step1: Perform polynomial long - division

We divide $x^{2}-x + 2$ by $x$. $\frac{x^{2}-x + 2}{x}=x - 1+\frac{2}{x}$.

Step2: Integrate term - by - term

$\int(x - 1+\frac{2}{x})dx=\int xdx-\int 1dx + 2\int\frac{1}{x}dx$.

Step3: Apply integration rules

We know that $\int xdx=\frac{x^{2}}{2}$, $\int 1dx=x$ and $\int\frac{1}{x}dx=\ln|x|$. So $\int xdx-\int 1dx + 2\int\frac{1}{x}dx=\frac{x^{2}}{2}-x + 2\ln|x|+C$.

Answer:

$\frac{x^{2}}{2}-x + 2\ln|x|+C$