integrate x^n — step-by-step solution

The expression:

x^{n}

contains several variables so we pick x for integration

Let's integrate:

\int x^{n} d x

We integrate

x^{n}

by applying:

\int x^{n} d x = \frac{x^{n + 1}}{n + 1}

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

\int x^{n} d x

\frac{x^{n + 1}}{n + 1}

\frac{x^{n + 1}}{n + 1}

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

\frac{x^{n + 1}}{n + 1} + C