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Derivative of:
e^x/(1+e^x)
Graphing y =:
e^x/(1+e^x)
Limit of the function:
e^x/(1+e^x)
Identical expressions
e^x/(one +e^x)
e to the power of x divide by (1 plus e to the power of x)
e to the power of x divide by (one plus e to the power of x)
ex/(1+ex)
ex/1+ex
e^x/1+e^x
e^x divide by (1+e^x)
e^x/(1+e^x)dx
Similar expressions
e^x/(1-e^x)

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

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

The solution

You have entered [src]

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

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

Integral(E^x/(1 + E^x), (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                     
 | 1 + E                      
 |                            
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-log(2) + log(1 + E)

$$- \log{\left(2 \right)} + \log{\left(1 + e \right)}$$

-log(2) + log(1 + E)

$$- \log{\left(2 \right)} + \log{\left(1 + e \right)}$$

-log(2) + log(1 + E)

Numerical answer [src]

0.620114506958278

0.620114506958278

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2