Evaluate the Integral integral of (2x^2+6x) with respect to x

$\int (2 x^{2} + 6 x) d x$

Remove parentheses.

$\int 2 x^{2} + 6 x d x$

Split the single integral into multiple integrals.

$\int 2 x^{2} d x + \int 6 x d x$

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

$2 \int x^{2} d x + \int 6 x d x$

By the Power Rule, the integral of $x^{2}$ with respect to $x$ is $\frac{1}{3} x^{3}$ .

$2 (\frac{1}{3} x^{3} + C) + \int 6 x d x$

Since $6$ is constant with respect to $x$ , move $6$ out of the integral.

$2 (\frac{1}{3} x^{3} + C) + 6 \int x d x$

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

$2 (\frac{1}{3} x^{3} + C) + 6 (\frac{1}{2} x^{2} + C)$

Simplify.

$2 (\frac{1}{3}) x^{3} + 6 (\frac{1}{2}) x^{2} + C$

Simplify.

Combine $2$ and $\frac{1}{3}$ .

$\frac{2}{3} x^{3} + 6 (\frac{1}{2}) x^{2} + C$

Combine $6$ and $\frac{1}{2}$ .

$\frac{2}{3} x^{3} + \frac{6}{2} x^{2} + C$

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6$ .

$\frac{2}{3} x^{3} + \frac{2 \cdot 3}{2} x^{2} + C$

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $3$ by $1$ .

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