2 plus the integral of x — step-by-step solution

⇥Let's integrate:

\int x d x

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

\int x d x

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

⇥

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

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

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

Let's calculate:

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

▶Result:

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

, with C being any constant