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Integral of d{x}:
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Identical expressions
(x+ three)e^4x
(x plus 3)e to the power of 4x
(x plus three)e to the power of 4x
(x+3)e4x
x+3e4x
(x+3)e⁴x
x+3e^4x
(x+3)e^4xdx
Similar expressions
(x-3)e^4x
What you mean?
(x + 3)*e^4*x
(x + 3)*e^(4*x)
(x + 3)*e^(4*x)

You entered:

(x+3)e^4x

What you mean?

(x + 3)*e^4*x

(x + 3)*e^(4*x)

(x + 3)*e^(4*x)

Integral of (x+3)e^4x dx

The solution

You have entered [src]

  2                
  /                
 |                 
 |           4     
 |  (x + 3)*E *x dx
 |                 
/                  
0

$$\int\limits_{0}^{2} x e^{4} \left(x + 3\right)\, dx$$

Integral(((x + 3)*E^4)*x, (x, 0, 2))

Detail solution

Rewrite the integrand:

$x e^{4} \left(x + 3\right) = x^{2} e^{4} + 3 x e^{4}$
Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int x^{2} e^{4}\, dx = e^{4} \int x^{2}\, dx$
  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: $\frac{x^{3} e^{4}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 3 x e^{4}\, dx = 3 e^{4} \int x\, dx$
  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: $\frac{3 x^{2} e^{4}}{2}$
The result is: $\frac{x^{3} e^{4}}{3} + \frac{3 x^{2} e^{4}}{2}$
Now simplify:

$\frac{x^{2} \left(2 x + 9\right) e^{4}}{6}$
Add the constant of integration:

$\frac{x^{2} \left(2 x + 9\right) e^{4}}{6}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(2 x + 9\right) e^{4}}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                     
 |                        3  4      2  4
 |          4            x *e    3*x *e 
 | (x + 3)*E *x dx = C + ----- + -------
 |                         3        2   
/

$$\int x e^{4} \left(x + 3\right)\, dx = C + \frac{x^{3} e^{4}}{3} + \frac{3 x^{2} e^{4}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

    4
26*e 
-----
  3

$$\frac{26 e^{4}}{3}$$

    4
26*e 
-----
  3

$$\frac{26 e^{4}}{3}$$

26*exp(4)/3

Numerical answer [src]

473.183966953917

473.183966953917

The graph

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

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What you mean?

Integral of (x+3)e^4x dx

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The solution