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Solving integrals/ exp^(3x)

Integral of exp^(3x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  2        
  /        
 |         
 |   3*x   
 |  E    dx
 |         
/          
0
$$\int\limits_{0}^{2} e^{3 x}\, dx$$ 
Integral(E^(3*x), (x, 0, 2))
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  
/
$$\int e^{3 x}\, dx = C + \frac{e^{3 x}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
       6
  1   e 
- - + --
  3   3
$$- \frac{1}{3} + \frac{e^{6}}{3}$$ 
=
= 
       6
  1   e 
- - + --
  3   3
$$- \frac{1}{3} + \frac{e^{6}}{3}$$ 
-1/3 + exp(6)/3
Numerical answer [src] 
134.142931164245
134.142931164245

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

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