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Identical expressions
(6x+ twelve - three)e^(twelve - two)x
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(6x plus twelve minus three)e to the power of (twelve minus two)x
(6x+12-3)e(12-2)x
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(6x+12-3)e^(12-2)xdx
Similar expressions
(6x-12-3)e^(12-2)x
(6x+12-3)e^(12+2)x
(6x+12+3)e^(12-2)x

Integral of (6x+12-3)e^(12-2)x dx

The solution

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  2                        
  /                        
 |                         
 |                  10     
 |  (6*x + 12 - 3)*E  *x dx
 |                         
/                          
0

$$\int\limits_{0}^{2} x e^{10} \left(\left(6 x + 12\right) - 3\right)\, dx$$

Integral(((6*x + 12 - 3)*E^10)*x, (x, 0, 2))

Detail solution

Rewrite the integrand:

$x e^{10} \left(\left(6 x + 12\right) - 3\right) = 6 x^{2} e^{10} + 9 x e^{10}$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 6 x^{2} e^{10}\, dx = 6 e^{10} \int x^{2}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  So, the result is: $2 x^{3} e^{10}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 9 x e^{10}\, dx = 9 e^{10} \int x\, dx$
  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: $\frac{9 x^{2} e^{10}}{2}$
The result is: $2 x^{3} e^{10} + \frac{9 x^{2} e^{10}}{2}$
Now simplify:

$\frac{x^{2} \left(4 x + 9\right) e^{10}}{2}$
Add the constant of integration:

$\frac{x^{2} \left(4 x + 9\right) e^{10}}{2}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(4 x + 9\right) e^{10}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                 
 |                                             2  10
 |                 10               3  10   9*x *e  
 | (6*x + 12 - 3)*E  *x dx = C + 2*x *e   + --------
 |                                             2    
/

$$\int x e^{10} \left(\left(6 x + 12\right) - 3\right)\, dx = C + 2 x^{3} e^{10} + \frac{9 x^{2} e^{10}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

    10
34*e

$$34 e^{10}$$

    10
34*e

$$34 e^{10}$$

34*exp(10)

Numerical answer [src]

748899.837023428

748899.837023428

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

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Integral of (6x+12-3)e^(12-2)x dx

Limits of integration:

The graph:

Piecewise:

The solution