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3^(2*x)
Solving integrals/ 3^(2*x)

Integral of 3^(2*x) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1        
  /        
 |         
 |   2*x   
 |  3    dx
 |         
/          
0
∫0132x dx\int\limits_{0}^{1} 3^{2 x}\, dx 
Integral(3^(2*x), (x, 0, 1))
Detail solution

  1. Let u=2xu = 2 x.

    Then let du=2dxdu = 2 dx and substitute du2\frac{du}{2}:

    ∫3u2 du\int \frac{3^{u}}{2}\, du

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

      ∫3u du=∫3u du2\int 3^{u}\, du = \frac{\int 3^{u}\, du}{2}

      1. The integral of an exponential function is itself divided by the natural logarithm of the base.

        ∫3u du=3ulog⁡(3)\int 3^{u}\, du = \frac{3^{u}}{\log{\left(3 \right)}}

      So, the result is: 3u2log⁡(3)\frac{3^{u}}{2 \log{\left(3 \right)}}

    Now substitute uu back in:

    32x2log⁡(3)\frac{3^{2 x}}{2 \log{\left(3 \right)}}

  2. Now simplify:

    9x2log⁡(3)\frac{9^{x}}{2 \log{\left(3 \right)}}

  3. Add the constant of integration:

    9x2log⁡(3)+constant\frac{9^{x}}{2 \log{\left(3 \right)}}+ \mathrm{constant}

The answer is:

9x2log⁡(3)+constant\frac{9^{x}}{2 \log{\left(3 \right)}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                      
 |                  2*x  
 |  2*x            3     
 | 3    dx = C + --------
 |               2*log(3)
/
∫32x dx=32x2log⁡(3)+C\int 3^{2 x}\, dx = \frac{3^{2 x}}{2 \log{\left(3 \right)}} + C
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90010
Plot the graph f(x)
The answer [src] 
  4   
------
log(3)
4log⁡(3)\frac{4}{\log{\left(3 \right)}} 
=
= 
  4   
------
log(3)
4log⁡(3)\frac{4}{\log{\left(3 \right)}} 
4/log(3)
Numerical answer [src] 
3.64095690650735
3.64095690650735
The graph
Integral of 3^(2*x) dx

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

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