Let's compute the integral: $\int \frac{x^3+2}{x^2}dx$

For $x$ ≠ 0, divide each numerator term by the power in the denominator: $\frac{x^3+2}{x^2}=x+\frac{2}{x^2}$

ⅰ $\int \frac{x^3+2}{x^2}dx$ = $\int xdx+\int \frac{2}{x^2}dx$

$\int xdx+\int \frac{2}{x^2}dx$

ⓘ An antiderivative of x^n is x^(n+1)/(n+1), for n ≠ -1: $\int xdx$ = $\frac{x^2}{2}$■A constant factor stays in front of the integral. An antiderivative of x^n is x^(n+1)/(n+1), for n ≠ -1: $\int \frac{2}{x^2}dx$ = $\int 2x^{-2}dx$ = $-2x^{-1}$ = $-\frac{2}{x}$

$\frac{x^2}{2}-\frac{2}{x}$

▶Indefinite integrals are defined up to an additive constant C, so this yields: $\frac{x^2}{2}-\frac{2}{x}+C$