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Solving integrals/ 7*2^x

Integral of 7*2^x dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
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∫017⋅2x dx\int\limits_{0}^{1} 7 \cdot 2^{x}\, dx 
Integral(7*2^x, (x, 0, 1))
Detail solution

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

    ∫7⋅2x dx=7∫2x dx\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.

      ∫2x dx=2xlog⁡(2)\int 2^{x}\, dx = \frac{2^{x}}{\log{\left(2 \right)}}

    So, the result is: 7⋅2xlog⁡(2)\frac{7 \cdot 2^{x}}{\log{\left(2 \right)}}

  2. Add the constant of integration:

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

The answer is:

7⋅2xlog⁡(2)+constant\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)
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∫7⋅2x dx=7⋅2xlog⁡(2)+C\int 7 \cdot 2^{x}\, dx = \frac{7 \cdot 2^{x}}{\log{\left(2 \right)}} + C
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90030
Plot the graph f(x)
The answer [src] 
  7   
------
log(2)
7log⁡(2)\frac{7}{\log{\left(2 \right)}} 
=
= 
  7   
------
log(2)
7log⁡(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.

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