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e^(6x)
Solving integrals/ e^(6x)

Integral of e^(6x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1        
  /        
 |         
 |   6*x   
 |  E    dx
 |         
/          
0
$$\int\limits_{0}^{1} e^{6 x}\, dx$$ 
Integral(E^(6*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] 
  /                  
 |                6*x
 |  6*x          e   
 | E    dx = C + ----
 |                6  
/
$$\int e^{6 x}\, dx = C + \frac{e^{6 x}}{6}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
       6
  1   e 
- - + --
  6   6
$$- \frac{1}{6} + \frac{e^{6}}{6}$$ 
=
= 
       6
  1   e 
- - + --
  6   6
$$- \frac{1}{6} + \frac{e^{6}}{6}$$ 
-1/6 + exp(6)/6
Numerical answer [src] 
67.0714655821225
67.0714655821225
The graph
Integral of e^(6x) dx

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

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