Mister Exam

Integral of e^(3x) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1        
  /        
 |         
 |   3*x   
 |  E    dx
 |         
/          
0          
$$\int\limits_{0}^{1} e^{3 x}\, dx$$
Integral(E^(3*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]
  /                  
 |                3*x
 |  3*x          e   
 | E    dx = C + ----
 |                3  
/                    
$$\int e^{3 x}\, dx = C + \frac{e^{3 x}}{3}$$
The graph
The answer [src]
       3
  1   e 
- - + --
  3   3 
$$- \frac{1}{3} + \frac{e^{3}}{3}$$
=
=
       3
  1   e 
- - + --
  3   3 
$$- \frac{1}{3} + \frac{e^{3}}{3}$$
-1/3 + exp(3)/3
Numerical answer [src]
6.36184564106256
6.36184564106256
The graph
Integral of e^(3x) dx

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