Monique Slaughter

2022-01-04

Find the integral, full solution
$\int {\left(2x+3\right)}^{2}dx$

### Answer & Explanation

Mary Herrera

Step 1
Given integral,
$\int {\left(2x+3\right)}^{2}dx$
Step 2
$\int {\left(2x+3\right)}^{2}dx=\int \left(4{x}^{2}+12x+9\right)dx$
$=\int 4{x}^{2}dx+\int 12xdx+\int 9dx$
$=4\int {x}^{2}dx+12\int xdx+9\int dx$
$=4\frac{{x}^{3}}{3}+12\frac{{x}^{2}}{2}+9x+C$ Since
$=\frac{4{x}^{3}}{3}+6{x}^{2}+9x+C$

Raymond Foley

Calculate:
$\int {\left(2x+3\right)}^{2}dx$
$=\frac{1}{2}\int {u}^{2}du$
$\int {u}^{2}du$
$=\frac{{u}^{3}}{3}$
$\frac{1}{2}\int {u}^{2}du$
$=\frac{{u}^{3}}{6}$
$=\frac{{\left(2x+3\right)}^{3}}{6}$
$=\frac{{\left(2x+3\right)}^{3}}{6}+C$
Lets

karton

$\int \left(2x+3{\right)}^{2}dx\phantom{\rule{0ex}{0ex}}\int 4{x}^{2}+12x+9dx\phantom{\rule{0ex}{0ex}}\int 4{x}^{2}dx+\int 12xdx+\int 9dx\phantom{\rule{0ex}{0ex}}\frac{4{x}^{3}}{3}+6{x}^{2}+9x\phantom{\rule{0ex}{0ex}}\text{Add C}\phantom{\rule{0ex}{0ex}}\text{Answer:}\phantom{\rule{0ex}{0ex}}\frac{4{x}^{3}}{3}+6{x}^{2}+9x+C$