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Integral of 2*3^x dx

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

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

Detail solution

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

$\int 2 \cdot 3^{x}\, dx = 2 \int 3^{x}\, dx$
1. The integral of an exponential function is itself divided by the natural logarithm of the base.
  
  $\int 3^{x}\, dx = \frac{3^{x}}{\log{\left(3 \right)}}$
So, the result is: $\frac{2 \cdot 3^{x}}{\log{\left(3 \right)}}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

  4   
------
log(3)

$$\frac{4}{\log{\left(3 \right)}}$$

  4   
------
log(3)

$$\frac{4}{\log{\left(3 \right)}}$$

4/log(3)

Numerical answer [src]

3.64095690650735

3.64095690650735

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