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3^(2x-1)

Integral of 3^(2x-1) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  1            
  /            
 |             
 |   2*x - 1   
 |  3        dx
 |             
/              
0              
$$\int\limits_{0}^{1} 3^{2 x - 1}\, dx$$
Integral(3^(2*x - 1), (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

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

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

        So, the result is:

      Now substitute back in:

    Method #2

    1. Rewrite the integrand:

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

      1. Let .

        Then let and substitute :

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

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

          So, the result is:

        Now substitute back in:

      So, the result is:

    Method #3

    1. Rewrite the integrand:

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

      1. Let .

        Then let and substitute :

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

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

          So, the result is:

        Now substitute back in:

      So, the result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                          
 |                    2*x - 1
 |  2*x - 1          3       
 | 3        dx = C + --------
 |                   2*log(3)
/                            
$$\int 3^{2 x - 1}\, dx = \frac{3^{2 x - 1}}{2 \log{\left(3 \right)}} + C$$
The graph
The answer [src]
   4    
--------
3*log(3)
$$\frac{4}{3 \log{\left(3 \right)}}$$
=
=
   4    
--------
3*log(3)
$$\frac{4}{3 \log{\left(3 \right)}}$$
4/(3*log(3))
Numerical answer [src]
1.21365230216912
1.21365230216912
The graph
Integral of 3^(2x-1) dx

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