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e^(2*x)

Integral of e^(2*x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1        
  /        
 |         
 |   2*x   
 |  E    dx
 |         
/          
0          
01e2xdx\int\limits_{0}^{1} e^{2 x}\, dx
Integral(E^(2*x), (x, 0, 1))
Detail solution
  1. Let u=2xu = 2 x.

    Then let du=2dxdu = 2 dx and substitute du2\frac{du}{2}:

    eu2du\int \frac{e^{u}}{2}\, du

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

      False\text{False}

      1. The integral of the exponential function is itself.

        eudu=eu\int e^{u}\, du = e^{u}

      So, the result is: eu2\frac{e^{u}}{2}

    Now substitute uu back in:

    e2x2\frac{e^{2 x}}{2}

  2. Add the constant of integration:

    e2x2+constant\frac{e^{2 x}}{2}+ \mathrm{constant}


The answer is:

e2x2+constant\frac{e^{2 x}}{2}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                  
 |                2*x
 |  2*x          e   
 | E    dx = C + ----
 |                2  
/                    
e2xdx=C+e2x2\int e^{2 x}\, dx = C + \frac{e^{2 x}}{2}
The graph
0.001.000.100.200.300.400.500.600.700.800.90010
The answer [src]
       2
  1   e 
- - + --
  2   2 
12+e22- \frac{1}{2} + \frac{e^{2}}{2}
=
=
       2
  1   e 
- - + --
  2   2 
12+e22- \frac{1}{2} + \frac{e^{2}}{2}
-1/2 + exp(2)/2
Numerical answer [src]
3.19452804946533
3.19452804946533
The graph
Integral of e^(2*x) dx

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