Question

Find the integral of $\int \frac{x^3+5x^2-4}{x^2}dx$

Answer 1

$\int \frac{x^3+5x^2-4}{x^2}dx$

$=\int (x+5-4x^{-2})dx$

$=\int xdx+5\int 1.dx-4\int x^{-2}dx$

$=\frac{x^2}{2}+5x-4\left(\frac{x^{-1}}{-1}\right)+C$

$=\frac{x^2}{2}+5x+\frac{4}{x}+C$