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Integral of d{x}:
Integral of x*e^(x*(-2))
Integral of 1/(2+3x^2)
Integral of x^2*e^2
Integral of x^0.5
Derivative of:
5*e^(2*x)
Identical expressions
five *e^(two *x)
5 multiply by e to the power of (2 multiply by x)
five multiply by e to the power of (two multiply by x)
5*e(2*x)
5*e2*x
5e^(2x)
5e(2x)
5e2x
5e^2x
5*e^(2*x)dx

Solving integrals/ 5*e^(2*x)

Integral of 5e^(2x) dx

The solution

You have entered [src]

  1          
  /          
 |           
 |     2*x   
 |  5*E    dx
 |           
/            
0

$$\int\limits_{0}^{1} 5 e^{2 x}\, dx$$

Integral(5*E^(2*x), (x, 0, 1))

Detail solution

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

$\int 5 e^{2 x}\, dx = 5 \int e^{2 x}\, dx$
1. Let $u = 2 x$ .
  
  Then let $du = 2 dx$ and substitute $\frac{du}{2}$ :
  
  $\int \frac{e^{u}}{2}\, du$
  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: $\frac{e^{u}}{2}$
  Now substitute $u$ back in:
  
  $\frac{e^{2 x}}{2}$
So, the result is: $\frac{5 e^{2 x}}{2}$
Add the constant of integration:

$\frac{5 e^{2 x}}{2}+ \mathrm{constant}$

The answer is:

$\frac{5 e^{2 x}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                    2*x
 |    2*x          5*e   
 | 5*E    dx = C + ------
 |                   2   
/

$$\int 5 e^{2 x}\, dx = C + \frac{5 e^{2 x}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

         2
  5   5*e 
- - + ----
  2    2

$$- \frac{5}{2} + \frac{5 e^{2}}{2}$$

=

         2
  5   5*e 
- - + ----
  2    2

$$- \frac{5}{2} + \frac{5 e^{2}}{2}$$

-5/2 + 5*exp(2)/2

Numerical answer [src]

15.9726402473266

15.9726402473266

The graph

Integral of 5*e^(2*x) dx

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