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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1        
  /        
 |         
 |   2*x   
 |  E      
 |  ---- dx
 |   2     
 |         
/          
0
∫01e2x2 dx\int\limits_{0}^{1} \frac{e^{2 x}}{2}\, dx 
Integral(E^(2*x)/2, (x, 0, 1))
Detail solution

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

    ∫e2x2 dx=∫e2x dx2\int \frac{e^{2 x}}{2}\, dx = \frac{\int e^{2 x}\, dx}{2}

    1. Let u=2xu = 2 x.

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

      ∫eu2 du\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.

          ∫eu du=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}

    So, the result is: e2x4\frac{e^{2 x}}{4}

  2. Add the constant of integration:

    e2x4+constant\frac{e^{2 x}}{4}+ \mathrm{constant}

The answer is:

e2x4+constant\frac{e^{2 x}}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                  
 |                   
 |  2*x           2*x
 | E             e   
 | ---- dx = C + ----
 |  2             4  
 |                   
/
∫e2x2 dx=C+e2x4\int \frac{e^{2 x}}{2}\, dx = C + \frac{e^{2 x}}{4}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9005
Plot the graph f(x)
The answer [src] 
       2
  1   e 
- - + --
  4   4
−14+e24- \frac{1}{4} + \frac{e^{2}}{4} 
=
= 
       2
  1   e 
- - + --
  4   4
−14+e24- \frac{1}{4} + \frac{e^{2}}{4} 
-1/4 + exp(2)/4
Numerical answer [src] 
1.59726402473266
1.59726402473266
The graph
Integral of e^(2*x)/2 dx

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

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