Evaluate the Integral integral of (2x+3) with respect to x

$\int (2 x + 3) d x$

Remove parentheses.

$\int 2 x + 3 d x$

Split the single integral into multiple integrals.

$\int 2 x d x + \int 3 d x$

Since $2$ is constant with respect to $x$ , move $2$ out of the integral.

$2 \int x d x + \int 3 d x$

By the Power Rule, the integral of $x$ with respect to $x$ is $\frac{1}{2} x^{2}$ .

$2 (\frac{1}{2} x^{2} + C) + \int 3 d x$

Apply the constant rule.

$2 (\frac{1}{2} x^{2} + C) + 3 x + C$

Simplify.

Combine $\frac{1}{2}$ and $x^{2}$ .

$2 (\frac{x^{2}}{2} + C) + 3 x + C$

Simplify.

$x^{2} + 3 x + C$