Mister Exam

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How to use it?
Integral of d{x}:
Integral of 0dx
Integral of x^(4/5)
Integral of dr/r
Integral of 1/sqrt(x^2-5)
Limit of the function:
e^(2+x)
Identical expressions
e^(two +x)
e to the power of (2 plus x)
e to the power of (two plus x)
e(2+x)
e2+x
e^2+x
e^(2+x)dx
Similar expressions
e^(2-x)

Solving integrals/ e^(2+x)

Integral of e^(2+x) dx

The solution

You have entered [src]

 oo          
  /          
 |           
 |   2 + x   
 |  E      dx
 |           
/            
0

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

Integral(E^(2 + x), (x, 0, oo))

Detail solution

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

$e^{x + 2}+ \mathrm{constant}$

The answer is:

$e^{x + 2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                       
 |  2 + x           2 + x
 | E      dx = C + e     
 |                       
/

$$\int e^{x + 2}\, dx = C + e^{x + 2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

=

oo

$$\infty$$

oo

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