Mister Exam

Other calculators


1/(exp^x+exp^-x)

Integral of 1/(exp^x+exp^-x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

    Method #1

    1. Let .

      Then let and substitute :

      1. The integral of is .

      Now substitute back in:

    Method #2

    1. Rewrite the integrand:

    2. 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]
  /                            
 |                             
 |      1                  / x\
 | 1*-------- dx = C + atan\e /
 |    x    -x                  
 |   e  + e                    
 |                             
/                              
$$-\arctan e^ {- x }$$
The graph
The answer [src]
         /   2                         \          /   2                         \
- RootSum\4*z  + 1, i -> i*log(1 + 2*i)/ + RootSum\4*z  + 1, i -> i*log(3 + 2*i)/
$${{\pi}\over{4}}-\arctan \left({{1}\over{3}}\right)$$
=
=
         /   2                         \          /   2                         \
- RootSum\4*z  + 1, i -> i*log(1 + 2*i)/ + RootSum\4*z  + 1, i -> i*log(3 + 2*i)/
$$- \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + 1 \right)} \right)\right)} + \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + 3 \right)} \right)\right)}$$
Numerical answer [src]
0.463647609000806
0.463647609000806
The graph
Integral of 1/(exp^x+exp^-x) dx

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