Integral of (x+2)(x-3) dx

The solution

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 |  (x + 2)*(x - 3) dx
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$$\int\limits_{0}^{1} \left(x - 3\right) \left(x + 2\right)\, dx$$

Integral((x + 2)*(x - 3), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\left(x - 3\right) \left(x + 2\right) = x^{2} - x - 6$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x\right)\, dx = - \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $- \frac{x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-6\right)\, dx = - 6 x$
The result is: $\frac{x^{3}}{3} - \frac{x^{2}}{2} - 6 x$
Now simplify:

$\frac{x \left(2 x^{2} - 3 x - 36\right)}{6}$
Add the constant of integration:

$\frac{x \left(2 x^{2} - 3 x - 36\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{2} - 3 x - 36\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                2    3
 |                                x    x 
 | (x + 2)*(x - 3) dx = C - 6*x - -- + --
 |                                2    3 
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-37/6

$$- \frac{37}{6}$$

-37/6

$$- \frac{37}{6}$$

-37/6

Numerical answer [src]

-6.16666666666667

-6.16666666666667

The graph

Use the examples entering the upper and lower limits of integration.

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Integral of (x+2)(x-3) dx

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The solution