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exp(4*x)

Integral of exp(4*x) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  1        
  /        
 |         
 |   4*x   
 |  e    dx
 |         
/          
0          
01e4xdx\int\limits_{0}^{1} e^{4 x}\, dx
Integral(exp(4*x), (x, 0, 1))
Detail solution
  1. Let u=4xu = 4 x.

    Then let du=4dxdu = 4 dx and substitute du4\frac{du}{4}:

    eu4du\int \frac{e^{u}}{4}\, 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: eu4\frac{e^{u}}{4}

    Now substitute uu back in:

    e4x4\frac{e^{4 x}}{4}

  2. Add the constant of integration:

    e4x4+constant\frac{e^{4 x}}{4}+ \mathrm{constant}


The answer is:

e4x4+constant\frac{e^{4 x}}{4}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                  
 |                4*x
 |  4*x          e   
 | e    dx = C + ----
 |                4  
/                    
e4xdx=C+e4x4\int e^{4 x}\, dx = C + \frac{e^{4 x}}{4}
The graph
0.001.000.100.200.300.400.500.600.700.800.900100
The answer [src]
       4
  1   e 
- - + --
  4   4 
14+e44- \frac{1}{4} + \frac{e^{4}}{4}
=
=
       4
  1   e 
- - + --
  4   4 
14+e44- \frac{1}{4} + \frac{e^{4}}{4}
-1/4 + exp(4)/4
Numerical answer [src]
13.3995375082861
13.3995375082861
The graph
Integral of exp(4*x) dx

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