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Integral of d{x}:
Integral of x^2*e^(x^3)
Integral of sqrt(x^2+4)
Integral of (x^2)/(1+x^6)
Integral of x^3/(x^2+1)^2
Derivative of:
2*e^(2*x)
Graphing y =:
2*e^(2*x)
Limit of the function:
2*e^(2*x)
Identical expressions
two *e^(two *x)
2 multiply by e to the power of (2 multiply by x)
two multiply by e to the power of (two multiply by x)
2*e(2*x)
2*e2*x
2e^(2x)
2e(2x)
2e2x
2e^2x
2*e^(2*x)dx

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

Integral of 2e^(2x) dx

The solution

You have entered [src]

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

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

Integral(2*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:

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

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

The answer is:

e^{2 x}+ \mathrm{constant}

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

      2
-1 + e

-1 + e^{2}

=

      2
-1 + e

-1 + e^{2}

-1 + exp(2)

Numerical answer [src]

6.38905609893065

6.38905609893065

The graph

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

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