Expand the integral $\int\left(x^2+4x+4\right)dx$ into $3$ integrals using the sum rule for integrals, to then solve each integral separately
$\int x^2dx+\int4xdx+\int4dx$
Intermediate steps
3
The integral $\int x^2dx$ results in: $\frac{x^{3}}{3}$
$\frac{x^{3}}{3}$
Intermediate steps
4
The integral $\int4xdx$ results in: $2x^2$
$2x^2$
Intermediate steps
5
The integral $\int4dx$ results in: $4x$
$4x$
6
Gather the results of all integrals
$\frac{x^{3}}{3}+2x^2+4x$
7
As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$
$\frac{x^{3}}{3}+2x^2+4x+C_0$
Final answer to the problem
$\frac{x^{3}}{3}+2x^2+4x+C_0$
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Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.