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(exp^x)/(2+exp^(2x))

Integral of (exp^x)/(2+exp^(2x)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1            
  /            
 |             
 |      x      
 |     e       
 |  -------- dx
 |       2*x   
 |  2 + e      
 |             
/              
0              
$$\int\limits_{0}^{1} \frac{e^{x}}{e^{2 x} + 2}\, dx$$
Integral(E^x/(2 + E^(2*x)), (x, 0, 1))
Detail solution
  1. Let .

    Then let and substitute :

    1. The integral of is .

    Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                            /  ___  x\
 |                     ___     |\/ 2 *e |
 |     x             \/ 2 *atan|--------|
 |    e                        \   2    /
 | -------- dx = C + --------------------
 |      2*x                   2          
 | 2 + e                                 
 |                                       
/                                        
$${{\arctan \left({{e^{x}}\over{\sqrt{2}}}\right)}\over{\sqrt{2}}}$$
The graph
The answer [src]
         /   2                         \          /   2                         \
- RootSum\8*z  + 1, i -> i*log(1 + 4*i)/ + RootSum\8*z  + 1, i -> i*log(e + 4*i)/
$${{\arctan \left({{e}\over{\sqrt{2}}}\right)}\over{\sqrt{2}}}-{{ \arctan \left({{1}\over{\sqrt{2}}}\right)}\over{\sqrt{2}}}$$
=
=
         /   2                         \          /   2                         \
- RootSum\8*z  + 1, i -> i*log(1 + 4*i)/ + RootSum\8*z  + 1, i -> i*log(e + 4*i)/
$$- \operatorname{RootSum} {\left(8 z^{2} + 1, \left( i \mapsto i \log{\left(4 i + 1 \right)} \right)\right)} + \operatorname{RootSum} {\left(8 z^{2} + 1, \left( i \mapsto i \log{\left(4 i + e \right)} \right)\right)}$$
Numerical answer [src]
0.336294761863011
0.336294761863011
The graph
Integral of (exp^x)/(2+exp^(2x)) dx

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