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Integral of e^x/(e^x-2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

    Method #1

    1. Let .

      Then let and substitute :

      1. Let .

        Then let and substitute :

        1. The integral of is .

        Now substitute back in:

      Now substitute back in:

    Method #2

    1. Let .

      Then let and substitute :

      1. The integral of is .

      Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                            
 |                             
 |    x                        
 |   E                /      x\
 | ------ dx = C + log\-2 + E /
 |  x                          
 | E  - 2                      
 |                             
/                              
$$\int \frac{e^{x}}{e^{x} - 2}\, dx = C + \log{\left(e^{x} - 2 \right)}$$
The graph
The answer [src]
nan
$$\text{NaN}$$
=
=
nan
$$\text{NaN}$$
nan
Numerical answer [src]
-11.8764540370141
-11.8764540370141

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