Question

Find the following integral.
$\int \frac{x^3-1}{x^2}dx$.

Answer 1

$\int \frac{x^3-1}{x^2}dx\Rightarrow \int \frac{x^3}{x^2}dx-\int \frac{1}{x^2}dx\Rightarrow \int xdx-\int \frac{1}{x^2}dx\Rightarrow \frac{x^2}{2}-\int x^{-2}dx\Rightarrow \frac{x^2}{2}-\frac{x^{-1}}{-1}+c\frac{x^2}{2}+\frac{1}{x}+c$