Question

Evaluate : $\int \left(\frac{x^3-1}{x^2}\right)dx$

Answer 1

$\int \left(\frac{x^3-1}{x^2}\right)dx$

$=\int \frac{x^3}{x^2}dx-\int \frac{1}{x^2}dx$

$=\int xdx-\int x^{-2}dx$

$=\frac{x^2}{2}-\frac{x^{-2+1}}{-2+1}+c$ where $c$ is the constant of integration.

$=\frac{x^2}{2}+\frac{1}{x}+c$