integral of x+1/(x^2) — step-by-step solution

Let's integrate:

\int (x + \frac{1}{x^{2}}) d x

ⅰ

\int (x + \frac{1}{x^{2}}) d x

\int x d x + \int \frac{1}{x^{2}} d x

\int x d x + \int \frac{1}{x^{2}} d x

ⓘ An antiderivative of x^n is x^(n+1)/(n+1), for n ≠ -1:

\int x d x

\frac{x^{2}}{2}

\int \frac{1}{x^{2}} d x

\int x^{-2} d x

- x^{-1}

- \frac{1}{x}

\frac{x^{2}}{2} - \frac{1}{x}

▶Indefinite integrals are defined up to an additive constant C, so this yields:

\frac{x^{2}}{2} - \frac{1}{x} + C