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e^x/(e^x+2)
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e to the power of x divide by (e to the power of x plus 2)
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Similar expressions
e^x/(e^x-2)

Solving integrals/ e^x/(e^x+2)

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

The solution

You have entered [src]

  1          
  /          
 |           
 |     x     
 |    E      
 |  ------ dx
 |   x       
 |  E  + 2   
 |           
/            
0

$$\int\limits_{0}^{1} \frac{e^{x}}{e^{x} + 2}\, dx$$

Integral(E^x/(E^x + 2), (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 $du$ :
  
  $\int \frac{1}{u + 2}\, du$
  1. Let $u = u + 2$ .
    
    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:
    
    $\log{\left(u + 2 \right)}$
  Now substitute $u$ back in:
  
  $\log{\left(e^{x} + 2 \right)}$
Method #2
1. Let $u = e^{x} + 2$ .
  
  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:
  
  $\log{\left(e^{x} + 2 \right)}$
Now simplify:

$\log{\left(e^{x} + 2 \right)}$
Add the constant of integration:

$\log{\left(e^{x} + 2 \right)}+ \mathrm{constant}$

The answer is:

$\log{\left(e^{x} + 2 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                           
 |                            
 |    x                       
 |   E                /     x\
 | ------ dx = C + log\2 + E /
 |  x                         
 | E  + 2                     
 |                            
/

$$\int \frac{e^{x}}{e^{x} + 2}\, dx = C + \log{\left(e^{x} + 2 \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-log(3) + log(2 + E)

$$- \log{\left(3 \right)} + \log{\left(2 + e \right)}$$

-log(3) + log(2 + E)

$$- \log{\left(3 \right)} + \log{\left(2 + e \right)}$$

-log(3) + log(2 + E)

Numerical answer [src]

0.452832425263941

0.452832425263941

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/(e^x+2) dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2