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

Integral of e^(2x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1        
  /        
 |         
 |   2*x   
 |  E    dx
 |         
/          
0
$$\int\limits_{0}^{1} e^{2 x}\, dx$$ 
Integral(E^(2*x), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

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

      1. The integral of the exponential function is itself.

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                  
 |                2*x
 |  2*x          e   
 | E    dx = C + ----
 |                2  
/
$$\int e^{2 x}\, dx = C + \frac{e^{2 x}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
       2
  1   e 
- - + --
  2   2
$$- \frac{1}{2} + \frac{e^{2}}{2}$$ 
=
= 
       2
  1   e 
- - + --
  2   2
$$- \frac{1}{2} + \frac{e^{2}}{2}$$ 
-1/2 + exp(2)/2
Numerical answer [src] 
3.19452804946533
3.19452804946533
The graph
Integral of e^(2x) dx

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

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