Rewrite the integrand $\left(3x+5\right)\left(2x+3\right)$ in expanded form
$\int\left(6x^2+19x+15\right)dx$
3
Expand the integral $\int\left(6x^2+19x+15\right)dx$ into $3$ integrals using the sum rule for integrals, to then solve each integral separately
$\int6x^2dx+\int19xdx+\int15dx$
Intermediate steps
4
The integral $\int6x^2dx$ results in: $2x^{3}$
$2x^{3}$
Intermediate steps
5
The integral $\int19xdx$ results in: $\frac{19}{2}x^2$
$\frac{19}{2}x^2$
Intermediate steps
6
The integral $\int15dx$ results in: $15x$
$15x$
7
Gather the results of all integrals
$2x^{3}+\frac{19}{2}x^2+15x$
8
As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$
$2x^{3}+\frac{19}{2}x^2+15x+C_0$
Final answer to the problem
$2x^{3}+\frac{19}{2}x^2+15x+C_0$
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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.