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Integral of d{x}:
Integral of e^x/x
Integral of 1/e^x
Integral of cosx/(1-cosx)^3
Integral of xxx
Derivative of:
1/e^x
Graphing y =:
1/e^x
Identical expressions
one /e^x
1 divide by e to the power of x
one divide by e to the power of x
1/ex
1 divide by e^x
1/e^xdx
Similar expressions
(e^(x)*sqrt(e^x-1))/e^x+3
(e^(2*x)-1)/e^x

Solving integrals/ 1/e^x

Integral of 1/e^x dx

The solution

You have entered [src]

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

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

Detail solution

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                 
 |                  
 |   1            -x
 | 1*-- dx = C - e  
 |    x             
 |   e              
 |                  
/

$$-e^ {- x }$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

     -1
1 - e

$$1-e^ {- 1 }$$

=

     -1
1 - e

$$- \frac{1}{e} + 1$$

Simplify

Numerical answer [src]

0.632120558828558

0.632120558828558

The graph

Integral of 1/e^x dx

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