Question:
$\int \frac{x^{3}+5 x^{2}-4}{x^{2}} d x$
Solution:
$\int \frac{x^{3}+5 x^{2}-4}{x^{2}} d x$
$=\int\left(x+5-4 x^{-2}\right) d x$
$=\int x d x+5 \int 1 \cdot d x-4 \int x^{-2} d x$
$=\frac{x^{2}}{2}+5 x-4\left(\frac{x^{-1}}{-1}\right)+\mathrm{C}$
$=\frac{x^{2}}{2}+5 x+\frac{4}{x}+\mathrm{C}$