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e^(2x+3)

Integral of e^(2x+3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1            
  /            
 |             
 |   2*x + 3   
 |  E        dx
 |             
/              
0              
$$\int\limits_{0}^{1} e^{2 x + 3}\, dx$$
Integral(E^(2*x + 3), (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 the exponential function is itself.

        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 the exponential function is itself.

          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 the exponential function is itself.

          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 + 3
 |  2*x + 3          e       
 | E        dx = C + --------
 |                      2    
/                            
$$\int e^{2 x + 3}\, dx = C + \frac{e^{2 x + 3}}{2}$$
The graph
The answer [src]
 5    3
e    e 
-- - --
2    2 
$$- \frac{e^{3}}{2} + \frac{e^{5}}{2}$$
=
=
 5    3
e    e 
-- - --
2    2 
$$- \frac{e^{3}}{2} + \frac{e^{5}}{2}$$
exp(5)/2 - exp(3)/2
Numerical answer [src]
64.1638110896945
64.1638110896945
The graph
Integral of e^(2x+3) dx

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