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Integral of d{x}:
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Integral of e^(x+1)
Graphing y =:
e^(x+1)
Derivative of:
e^(x+1)
Identical expressions
e^(x+ one)
e to the power of (x plus 1)
e to the power of (x plus one)
e(x+1)
ex+1
e^x+1
e^(x+1)dx
Similar expressions
e^(x-1)

Solving integrals/ e^(x+1)

Integral of e^(x+1) dx

The solution

You have entered [src]

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

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

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

Detail solution

There are multiple ways to do this integral.
Method #1
1. Let $u = x + 1$ .
  
  Then let $du = dx$ 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:
  
  $e^{x + 1}$
Method #2
1. Rewrite the integrand:
  
  $e^{x + 1} = e e^{x}$
2. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int e e^{x}\, dx = e \int e^{x}\, dx$
  1. The integral of the exponential function is itself.
    
    $\int e^{x}\, dx = e^{x}$
  So, the result is: $e e^{x}$
Now simplify:

$e^{x + 1}$
Add the constant of integration:

$e^{x + 1}+ \mathrm{constant}$

The answer is:

$e^{x + 1}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                       
 |  x + 1           x + 1
 | E      dx = C + e     
 |                       
/

$$\int e^{x + 1}\, dx = C + e^{x + 1}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

      2
-E + e

$$- e + e^{2}$$

=

      2
-E + e

$$- e + e^{2}$$

-E + exp(2)

Numerical answer [src]

4.6707742704716

4.6707742704716

The graph

Integral of e^(x+1) dx

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