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Integral of d{x}:
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Integral of x^(33/10)/5
Integral of exp(x)/x
Integral of dx/x^6
Derivative of:
3*e^(2*x)
Identical expressions
three *e^(two *x)
3 multiply by e to the power of (2 multiply by x)
three multiply by e to the power of (two multiply by x)
3*e(2*x)
3*e2*x
3e^(2x)
3e(2x)
3e2x
3e^2x
3*e^(2*x)dx
Similar expressions
(4*x+3)*e^(2*x)*dx

Solving integrals/ 3*e^(2*x)

Integral of 3e^(2x) dx

The solution

You have entered [src]

  1          
  /          
 |           
 |     2*x   
 |  3*E    dx
 |           
/            
0

$$\int\limits_{0}^{1} 3 e^{2 x}\, dx$$

Integral(3*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:

$\int 3 e^{2 x}\, dx = 3 \int e^{2 x}\, dx$
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: $\frac{3 e^{2 x}}{2}$
Add the constant of integration:

$\frac{3 e^{2 x}}{2}+ \mathrm{constant}$

The answer is:

$\frac{3 e^{2 x}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$\int 3 e^{2 x}\, dx = C + \frac{3 e^{2 x}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

         2
  3   3*e 
- - + ----
  2    2

$$- \frac{3}{2} + \frac{3 e^{2}}{2}$$

=

         2
  3   3*e 
- - + ----
  2    2

$$- \frac{3}{2} + \frac{3 e^{2}}{2}$$

-3/2 + 3*exp(2)/2

Numerical answer [src]

9.58358414839597

9.58358414839597

The graph

Integral of 3*e^(2*x) dx

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