integrate x^2+1 — step-by-step solution

Let's compute the integral:

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

ⅰ

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

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

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

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

\int x^{2} d x

\frac{x^{3}}{3}

■The derivative of

x

1

, so

x

is an antiderivative of

1

\int 1 d x

x

\frac{x^{3}}{3} + x

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

\frac{x^{3}}{3} + x + C