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Integral of d{x}:
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Integral of 1/xdx
Integral of e^(3*x)/3
Derivative of:
e^x/(e^x-1)
Graphing y =:
e^x/(e^x-1)
Identical expressions
e^x/(e^x- one)
e to the power of x divide by (e to the power of x minus 1)
e to the power of x divide by (e to the power of x minus one)
ex/(ex-1)
ex/ex-1
e^x/e^x-1
e^x divide by (e^x-1)
e^x/(e^x-1)dx
Similar expressions
e^x/(e^x+1)

Solving integrals/ e^x/(e^x-1)

Integral of e^x/(e^x-1) dx

The solution

You have entered [src]

  1          
  /          
 |           
 |     x     
 |    E      
 |  ------ dx
 |   x       
 |  E  - 1   
 |           
/            
0

$$\int\limits_{0}^{1} \frac{e^{x}}{e^{x} - 1}\, dx$$

Integral(E^x/(E^x - 1), (x, 0, 1))

Detail solution

There are multiple ways to do this integral.
Method #1
1. Let $u = e^{x}$ .
  
  Then let $du = e^{x} dx$ and substitute $du$ :
  
  $\int \frac{1}{u - 1}\, du$
  1. Let $u = u - 1$ .
    
    Then let $du = du$ and substitute $du$ :
    
    $\int \frac{1}{u}\, du$
    1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
    Now substitute $u$ back in:
    
    $\log{\left(u - 1 \right)}$
  Now substitute $u$ back in:
  
  $\log{\left(e^{x} - 1 \right)}$
Method #2
1. Let $u = e^{x} - 1$ .
  
  Then let $du = e^{x} dx$ and substitute $du$ :
  
  $\int \frac{1}{u}\, du$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  Now substitute $u$ back in:
  
  $\log{\left(e^{x} - 1 \right)}$
Now simplify:

$\log{\left(e^{x} - 1 \right)}$
Add the constant of integration:

$\log{\left(e^{x} - 1 \right)}+ \mathrm{constant}$

The answer is:

$\log{\left(e^{x} - 1 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                            
 |                             
 |    x                        
 |   E                /      x\
 | ------ dx = C + log\-1 + E /
 |  x                          
 | E  - 1                      
 |                             
/

$$\int \frac{e^{x}}{e^{x} - 1}\, dx = C + \log{\left(e^{x} - 1 \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

44.6322563900987

44.6322563900987

The graph

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

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How to use it?

Identical expressions

Similar expressions

Integral of e^x/(e^x-1) dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2