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Solving integrals/ 1/(1+exp(y))

Integral of 1/(1+exp(y)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |    1      
 |  ------ dy
 |       y   
 |  1 + e    
 |           
/            
0
∫011ey+1 dy\int\limits_{0}^{1} \frac{1}{e^{y} + 1}\, dy 
Integral(1/(1 + exp(y)), (y, 0, 1))
The answer (Indefinite) [src] 
  /                            
 |                             
 |   1                /     -y\
 | ------ dy = C - log\1 + e  /
 |      y                      
 | 1 + e                       
 |                             
/
∫1ey+1 dy=C−log⁡(1+e−y)\int \frac{1}{e^{y} + 1}\, dy = C - \log{\left(1 + e^{- y} \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.901-1
Plot the graph f(x)
The answer [src] 
1 - log(1 + E) + log(2)
−log⁡(1+e)+log⁡(2)+1- \log{\left(1 + e \right)} + \log{\left(2 \right)} + 1 
=
= 
1 - log(1 + E) + log(2)
−log⁡(1+e)+log⁡(2)+1- \log{\left(1 + e \right)} + \log{\left(2 \right)} + 1 
1 - log(1 + E) + log(2)
Numerical answer [src] 
0.379885493041722
0.379885493041722

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

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