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Solving integrals/ 2^(3*x)

Integral of 2^(3*x) dx

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$$\int\limits_{0}^{1} 2^{3 x}\, dx$$

Integral(2^(3*x), (x, 0, 1))

Detail solution

Let $u = 3 x$ .

Then let $du = 3 dx$ and substitute $\frac{du}{3}$ :

$\int \frac{2^{u}}{3}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2^{u}\, du = \frac{\int 2^{u}\, du}{3}$
  1. The integral of an exponential function is itself divided by the natural logarithm of the base.
    
    $\int 2^{u}\, du = \frac{2^{u}}{\log{\left(2 \right)}}$
  So, the result is: $\frac{2^{u}}{3 \log{\left(2 \right)}}$
Now substitute $u$ back in:

$\frac{2^{3 x}}{3 \log{\left(2 \right)}}$
Now simplify:

$\frac{8^{x}}{3 \log{\left(2 \right)}}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                      
 |                  3*x  
 |  3*x            2     
 | 2    dx = C + --------
 |               3*log(2)
/

$$\int 2^{3 x}\, dx = \frac{2^{3 x}}{3 \log{\left(2 \right)}} + C$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

   7    
--------
3*log(2)

$$\frac{7}{3 \log{\left(2 \right)}}$$

   7    
--------
3*log(2)

$$\frac{7}{3 \log{\left(2 \right)}}$$

7/(3*log(2))

Numerical answer [src]

3.36628842874091

3.36628842874091

The graph

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