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Integral of d{x}:
Integral of (4x-x^2)dx
Integral of (2x+3)/(x^2-5x+6)
Integral of xcoskx
Integral of -xe^x
Derivative of:
3*e^(3*x)
Identical expressions
three *e^(three *x)
3 multiply by e to the power of (3 multiply by x)
three multiply by e to the power of (three multiply by x)
3*e(3*x)
3*e3*x
3e^(3x)
3e(3x)
3e3x
3e^3x
3*e^(3*x)dx

Solving integrals/ 3*e^(3*x)

Integral of 3e^(3x) dx

The solution

You have entered [src]

  1          
  /          
 |           
 |     3*x   
 |  3*E    dx
 |           
/            
0

$$\int\limits_{0}^{1} 3 e^{3 x}\, dx$$

Integral(3*E^(3*x), (x, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int 3 e^{3 x}\, dx = 3 \int e^{3 x}\, dx$
1. Let $u = 3 x$ .
  
  Then let $du = 3 dx$ and substitute $\frac{du}{3}$ :
  
  $\int \frac{e^{u}}{3}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\text{False}$
    1. The integral of the exponential function is itself.
      
      $\int e^{u}\, du = e^{u}$
    So, the result is: $\frac{e^{u}}{3}$
  Now substitute $u$ back in:
  
  $\frac{e^{3 x}}{3}$
So, the result is: $e^{3 x}$
Add the constant of integration:

$e^{3 x}+ \mathrm{constant}$

The answer is:

$e^{3 x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                    
 |                     
 |    3*x           3*x
 | 3*E    dx = C + e   
 |                     
/

$$\int 3 e^{3 x}\, dx = C + e^{3 x}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

      3
-1 + e

$$-1 + e^{3}$$

=

      3
-1 + e

$$-1 + e^{3}$$

-1 + exp(3)

Numerical answer [src]

19.0855369231877

19.0855369231877

The graph

Integral of 3*e^(3*x) dx

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