chezmarylou1i

2021-12-29

Calculate the integral. $\int \left({x}^{2}-3x+2\right)dx$

turtletalk75

Expert

Step 1
$\int \left({x}^{2}-3x+2\right)dx$
The integral is
Since the integration is indefinite; a constant of integration is to be added.
Step 2
Solve the integral.
$\int \left({x}^{2}-3x+2\right)dx=\int {x}^{2}dx-\int 3xdx+2\int dx$
$=\frac{{x}^{2}+1}{2+1}-3\cdot \frac{{x}^{1+1}}{1+1}+2\cdot \frac{{x}^{0+1}}{0+1}+C$
$=\frac{{x}^{3}}{3}-\frac{3{x}^{2}}{2}+2x+C$
Hence the integral is solved.

Jenny Bolton

Expert

$\int \left({x}^{2}-3x+2\right)dx$
$=\int {x}^{2}dx-3\int xdx+2\int 1dx$
$\int {x}^{2}dx$
$=\frac{{x}^{3}}{3}$
$\int xdx$
$=\frac{{x}^{2}}{2}$
$\int 1dx$
=x
$\int {x}^{2}dx-3\int xdx+2\int 1dx$
$=\frac{{x}^{3}}{3}-\frac{3{x}^{2}}{2}+2x$
$\int \left({x}^{2}-3x+2\right)dx$
$=\frac{{x}^{3}}{3}-\frac{3{x}^{2}}{2}+2x+C$
$=\frac{x\left(2{x}^{2}-9x+12\right)}{6}+C$

Vasquez

Expert

Given:
$\int {x}^{2}-3x+2dx$
Use rules
$\int {x}^{2}dx-\int 3xdx+\int 2dx$
Evaluate
$\frac{{x}^{3}}{3}-\frac{3{x}^{2}}{2}+2x$
Add $C\in \mathbb{R}$
Solution:
$\frac{{x}^{3}}{3}-\frac{3{x}^{2}}{2}+2x+C,C\in \mathbb{R}$

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