Question

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

Answer 1

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

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

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

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

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