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Integral of d{x}:
Integral of 1÷(1+x^2)
Integral of e^(2*x)/(e^x+1)
Integral of dx/x^3
Integral of x/x
Identical expressions
e^(two *x)/(e^x+ one)
e to the power of (2 multiply by x) divide by (e to the power of x plus 1)
e to the power of (two multiply by x) divide by (e to the power of x plus one)
e(2*x)/(ex+1)
e2*x/ex+1
e^(2x)/(e^x+1)
e(2x)/(ex+1)
e2x/ex+1
e^2x/e^x+1
e^(2*x) divide by (e^x+1)
e^(2*x)/(e^x+1)dx
Similar expressions
e^(2*x)/(e^x-1)
What you mean?
e^(2*x)/(e^x + 1)
e^(2*x)/(e^x) + 1
e^(2*x)*x/e + 1
e^(2*x)/(e^x) + 1
e*2*x/(e^x + 1)
e*2*x/e^x + 1
e^(2*x)/(e^x) + 1

You entered:

e^(2*x)/(e^x+1)

What you mean?

e^(2*x)/(e^x + 1)

e^(2*x)/(e^x) + 1

e^(2*x)*x/e + 1

e^(2*x)/(e^x) + 1

e*2*x/(e^x + 1)

e*2*x/e^x + 1

e^(2*x)/(e^x) + 1

Integral of e^(2*x)/(e^x+1) dx

The solution

You have entered [src]

  1          
  /          
 |           
 |    2*x    
 |   e       
 |  ------ dx
 |   x       
 |  e  + 1   
 |           
/            
0

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

Integral(E^(2*x)/(E^x + 1), (x, 0, 1))

Detail solution

Let $u = e^{x}$ .

Then let $du = e^{x} dx$ and substitute $du$ :

$\int \frac{u}{u + 1}\, du$
1. Rewrite the integrand:
  
  $\frac{u}{u + 1} = 1 - \frac{1}{u + 1}$
2. Integrate term-by-term:
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 1\, du = u$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- \frac{1}{u + 1}\right)\, du = - \int \frac{1}{u + 1}\, du$
    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:
      
      $\log{\left(u + 1 \right)}$
    So, the result is: $- \log{\left(u + 1 \right)}$
  The result is: $u - \log{\left(u + 1 \right)}$
Now substitute $u$ back in:

$e^{x} - \log{\left(e^{x} + 1 \right)}$
Now simplify:

$e^{x} - \log{\left(e^{x} + 1 \right)}$
Add the constant of integration:

$e^{x} - \log{\left(e^{x} + 1 \right)}+ \mathrm{constant}$

The answer is:

$e^{x} - \log{\left(e^{x} + 1 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                
 |                                 
 |   2*x                           
 |  e               x      /     x\
 | ------ dx = C + e  - log\1 + e /
 |  x                              
 | e  + 1                          
 |                                 
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1 + e - log(1 + e) + log(2)

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

-1 + e - log(1 + e) + log(2)

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

Simplify

Numerical answer [src]

1.09816732150077

1.09816732150077

The graph

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

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Identical expressions

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What you mean?

Integral of e^(2*x)/(e^x+1) dx

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The graph:

Piecewise:

The solution