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Integral of d{x}:
Integral of x^(-1/2)
Integral of sin²xcos²x
Integral of x*2^(-x)
Integral of y^(-2/3)
Identical expressions
e^-x/2e^(-2x)
e to the power of minus x divide by 2e to the power of ( minus 2x)
e-x/2e(-2x)
e-x/2e-2x
e^-x/2e^-2x
e^-x divide by 2e^(-2x)
e^-x/2e^(-2x)dx
Similar expressions
e^-x/2e^(2x)
e^+x/2e^(-2x)
What you mean?
1/(e^(1*x)*2*e^(2*x))
e^(-x/2)/e^(2*x)
e^(-x/2)/e^(2*x)

You entered:

e^-x/2e^(-2x)

What you mean?

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

e^(-x/2)/e^(2*x)

e^(-x/2)/e^(2*x)

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

The solution

You have entered [src]

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

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

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

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{e^{- 2 x} e^{- x}}{2}\, dx = \frac{\int e^{- 2 x} e^{- x}\, dx}{2}$
1. Let $u = e^{- x}$ .
  
  Then let $du = - e^{- x} dx$ and substitute $- du$ :
  
  $\int u^{2}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- u^{2}\right)\, du = - \int u^{2}\, du$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int u^{2}\, du = \frac{u^{3}}{3}$
    So, the result is: $- \frac{u^{3}}{3}$
  Now substitute $u$ back in:
  
  $- \frac{e^{- 3 x}}{3}$
So, the result is: $- \frac{e^{- 3 x}}{6}$
Add the constant of integration:

$- \frac{e^{- 3 x}}{6}+ \mathrm{constant}$

The answer is:

$- \frac{e^{- 3 x}}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                        
 |                         
 |  -x  -2*x           -3*x
 | e  *e              e    
 | --------- dx = C - -----
 |     2                6  
 |                         
/

$$-{{e^ {- 3\,x }}\over{6}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

     -3
1   e  
- - ---
6    6

$${{{{1}\over{3}}-{{e^ {- 3 }}\over{3}}}\over{2}}$$

     -3
1   e  
- - ---
6    6

$$- \frac{1}{6 e^{3}} + \frac{1}{6}$$

Simplify

Numerical answer [src]

0.158368821938689

0.158368821938689

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^-x/2e^(-2x) dx

Limits of integration:

The graph:

Piecewise:

The solution