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Integral of 7*2^x dx

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$$\int\limits_{0}^{1} 7 \cdot 2^{x}\, dx$$

Integral(7*2^x, (x, 0, 1))

Detail solution

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

$\int 7 \cdot 2^{x}\, dx = 7 \int 2^{x}\, dx$
1. The integral of an exponential function is itself divided by the natural logarithm of the base.
  
  $\int 2^{x}\, dx = \frac{2^{x}}{\log{\left(2 \right)}}$
So, the result is: $\frac{7 \cdot 2^{x}}{\log{\left(2 \right)}}$
Add the constant of integration:

$\frac{7 \cdot 2^{x}}{\log{\left(2 \right)}}+ \mathrm{constant}$

The answer is:

$\frac{7 \cdot 2^{x}}{\log{\left(2 \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                    
 |                   x 
 |    x           7*2  
 | 7*2  dx = C + ------
 |               log(2)
/

$$\int 7 \cdot 2^{x}\, dx = \frac{7 \cdot 2^{x}}{\log{\left(2 \right)}} + C$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  7   
------
log(2)

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

  7   
------
log(2)

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

7/log(2)

Numerical answer [src]

10.0988652862227

10.0988652862227

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