Integral of 2^xdx dx

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

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

Detail solution

Let $u = 2^{x}$ .

Then let $du = 2^{x} \log{\left(2 \right)} dx$ and substitute $\frac{du}{\log{\left(2 \right)}}$ :

$\int \frac{1}{\log{\left(2 \right)}^{2}}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{\log{\left(2 \right)}}\, du = \frac{\int 1\, du}{\log{\left(2 \right)}}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 1\, du = u$
  So, the result is: $\frac{u}{\log{\left(2 \right)}}$
Now substitute $u$ back in:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                    
 |                  x  
 |  x              2   
 | 2 *1 dx = C + ------
 |               log(2)
/

$${{2^{x}}\over{\log 2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  1   
------
log(2)

$${{1}\over{\log 2}}$$

  1   
------
log(2)

$$\frac{1}{\log{\left(2 \right)}}$$

Simplify

Numerical answer [src]

1.44269504088896

1.44269504088896

The graph

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