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Identical expressions
e^(x+e^x)
e to the power of (x plus e to the power of x)
e(x+ex)
ex+ex
e^x+e^x
e^(x+e^x)dx
Similar expressions
e^(x-e^x)

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

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

The solution

You have entered [src]

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

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

Integral(E^(x + E^x), (x, 0, 1))

Detail solution

There are multiple ways to do this integral.
Method #1
1. Rewrite the integrand:
  
  $e^{e^{x} + x} = e^{x} e^{e^{x}}$
2. Let $u = e^{x}$ .
  
  Then let $du = e^{x} dx$ and substitute $du$ :
  
  $\int e^{u}\, du$
  1. The integral of the exponential function is itself.
    
    $\int e^{u}\, du = e^{u}$
  Now substitute $u$ back in:
  
  $e^{e^{x}}$
Method #2
1. Rewrite the integrand:
  
  $e^{e^{x} + x} = e^{x} e^{e^{x}}$
2. Let $u = e^{x}$ .
  
  Then let $du = e^{x} dx$ and substitute $du$ :
  
  $\int e^{u}\, du$
  1. The integral of the exponential function is itself.
    
    $\int e^{u}\, du = e^{u}$
  Now substitute $u$ back in:
  
  $e^{e^{x}}$
Add the constant of integration:

$e^{e^{x}}+ \mathrm{constant}$

The answer is:

$e^{e^{x}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                       
 |       x           / x\
 |  x + E            \e /
 | E       dx = C + e    
 |                       
/

$$\int e^{e^{x} + x}\, dx = C + e^{e^{x}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

      E
-E + e

$$- e + e^{e}$$

      E
-E + e

$$- e + e^{e}$$

-E + exp(E)

Numerical answer [src]

12.4359804130202

12.4359804130202

The graph

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2