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e^(8x)
Solving integrals/ e^(8x)

Integral of e^(8x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1        
  /        
 |         
 |   8*x   
 |  E    dx
 |         
/          
0
∫01e8x dx\int\limits_{0}^{1} e^{8 x}\, dx 
Integral(E^(8*x), (x, 0, 1))
Detail solution

  1. Let u=8xu = 8 x.

    Then let du=8dxdu = 8 dx and substitute du8\frac{du}{8}:

    ∫eu8 du\int \frac{e^{u}}{8}\, 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.

        ∫eu du=eu\int e^{u}\, du = e^{u}

      So, the result is: eu8\frac{e^{u}}{8}

    Now substitute uu back in:

    e8x8\frac{e^{8 x}}{8}

  2. Add the constant of integration:

    e8x8+constant\frac{e^{8 x}}{8}+ \mathrm{constant}

The answer is:

e8x8+constant\frac{e^{8 x}}{8}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                  
 |                8*x
 |  8*x          e   
 | E    dx = C + ----
 |                8  
/
∫e8x dx=C+e8x8\int e^{8 x}\, dx = C + \frac{e^{8 x}}{8}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9005000
Plot the graph f(x)
The answer [src] 
       8
  1   e 
- - + --
  8   8
−18+e88- \frac{1}{8} + \frac{e^{8}}{8} 
=
= 
       8
  1   e 
- - + --
  8   8
−18+e88- \frac{1}{8} + \frac{e^{8}}{8} 
-1/8 + exp(8)/8
Numerical answer [src] 
372.494748380216
372.494748380216
The graph
Integral of e^(8x) dx

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

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