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2^(3*x)
Solving integrals/ 2^(3*x)

Integral of 2^(3*x) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1        
  /        
 |         
 |   3*x   
 |  2    dx
 |         
/          
0
∫0123x dx\int\limits_{0}^{1} 2^{3 x}\, dx 
Integral(2^(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}:

    ∫2u3 du\int \frac{2^{u}}{3}\, du

    1. The integral of a constant times a function is the constant times the integral of the function:

      ∫2u du=∫2u du3\int 2^{u}\, du = \frac{\int 2^{u}\, du}{3}

      1. The integral of an exponential function is itself divided by the natural logarithm of the base.

        ∫2u du=2ulog⁡(2)\int 2^{u}\, du = \frac{2^{u}}{\log{\left(2 \right)}}

      So, the result is: 2u3log⁡(2)\frac{2^{u}}{3 \log{\left(2 \right)}}

    Now substitute uu back in:

    23x3log⁡(2)\frac{2^{3 x}}{3 \log{\left(2 \right)}}

  2. Now simplify:

    8x3log⁡(2)\frac{8^{x}}{3 \log{\left(2 \right)}}

  3. Add the constant of integration:

    8x3log⁡(2)+constant\frac{8^{x}}{3 \log{\left(2 \right)}}+ \mathrm{constant}

The answer is:

8x3log⁡(2)+constant\frac{8^{x}}{3 \log{\left(2 \right)}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                      
 |                  3*x  
 |  3*x            2     
 | 2    dx = C + --------
 |               3*log(2)
/
∫23x dx=23x3log⁡(2)+C\int 2^{3 x}\, dx = \frac{2^{3 x}}{3 \log{\left(2 \right)}} + C
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90010
Plot the graph f(x)
The answer [src] 
   7    
--------
3*log(2)
73log⁡(2)\frac{7}{3 \log{\left(2 \right)}} 
=
= 
   7    
--------
3*log(2)
73log⁡(2)\frac{7}{3 \log{\left(2 \right)}} 
7/(3*log(2))
Numerical answer [src] 
3.36628842874091
3.36628842874091
The graph
Integral of 2^(3*x) dx

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

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