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e^(3*x)

Integral of e^(3*x) dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src]
  1        
  /        
 |         
 |   3*x   
 |  E    dx
 |         
/          
0          
01e3xdx\int\limits_{0}^{1} e^{3 x}\, dx
Integral(E^(3*x), (x, 0, 1))
Detail solution
  1. Let u=3xu = 3 x.

    Then let du=3dxdu = 3 dx and substitute du3\frac{du}{3}:

    eu3du\int \frac{e^{u}}{3}\, 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: eu3\frac{e^{u}}{3}

    Now substitute uu back in:

    e3x3\frac{e^{3 x}}{3}

  2. Add the constant of integration:

    e3x3+constant\frac{e^{3 x}}{3}+ \mathrm{constant}


The answer is:

e3x3+constant\frac{e^{3 x}}{3}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                  
 |                3*x
 |  3*x          e   
 | E    dx = C + ----
 |                3  
/                    
e3xdx=C+e3x3\int e^{3 x}\, dx = C + \frac{e^{3 x}}{3}
The graph
0.001.000.100.200.300.400.500.600.700.800.90040
The answer [src]
       3
  1   e 
- - + --
  3   3 
13+e33- \frac{1}{3} + \frac{e^{3}}{3}
=
=
       3
  1   e 
- - + --
  3   3 
13+e33- \frac{1}{3} + \frac{e^{3}}{3}
-1/3 + exp(3)/3
Numerical answer [src]
6.36184564106256
6.36184564106256
The graph
Integral of e^(3*x) dx

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