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Identical expressions
(x- three)(x- two)
(x minus 3)(x minus 2)
(x minus three)(x minus two)
x-3x-2
(x-3)(x-2)dx
Similar expressions
(x+3)(x-2)
(x-3)(x+2)
y=lnx-3x-2

Solving integrals/ (x-3)(x-2)

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

The solution

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  1                   
  /                   
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 |  (x - 3)*(x - 2) dx
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0

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

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

Detail solution

Rewrite the integrand:

$\left(x - 3\right) \left(x - 2\right) = x^{2} - 5 x + 6$
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:
  
  $\int \left(- 5 x\right)\, dx = - 5 \int x\, dx$
  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: $- \frac{5 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 6\, dx = 6 x$
The result is: $\frac{x^{3}}{3} - \frac{5 x^{2}}{2} + 6 x$
Now simplify:

$\frac{x \left(2 x^{2} - 15 x + 36\right)}{6}$
Add the constant of integration:

$\frac{x \left(2 x^{2} - 15 x + 36\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{2} - 15 x + 36\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  2    3
 |                                5*x    x 
 | (x - 3)*(x - 2) dx = C + 6*x - ---- + --
 |                                 2     3 
/

$$\int \left(x - 3\right) \left(x - 2\right)\, dx = C + \frac{x^{3}}{3} - \frac{5 x^{2}}{2} + 6 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

23/6

$$\frac{23}{6}$$

23/6

$$\frac{23}{6}$$

23/6

Numerical answer [src]

3.83333333333333

3.83333333333333

The graph

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

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

Limits of integration:

The graph:

Piecewise:

The solution