Mister Exam

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How to use it?
Integral of d{x}:
Integral of -e^-x
Integral of tan^5(x)
Integral of sec(x)tan(x)
Integral of (7x-15)/(x^3+2x^2+5x)
Graphing y =:
-e^-x
Derivative of:
-e^-x
Identical expressions
-e^-x
minus e to the power of minus x
-e-x
-e^-xdx
Similar expressions
e^-x
-e^+x

Solving integrals/ -e^-x

Integral of -e^-x dx

The solution

You have entered [src]

$$\int\limits_{0}^{1} \left(- e^{- x}\right)\, dx$$

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

Detail solution

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

$\int \left(- e^{- x}\right)\, dx = - \int e^{- x}\, dx$
1. Let $u = - x$ .
  
  Then let $du = - dx$ and substitute $- du$ :
  
  $\int \left(- e^{u}\right)\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\text{False}$
    1. The integral of the exponential function is itself.
      
      $\int e^{u}\, du = e^{u}$
    So, the result is: $- e^{u}$
  Now substitute $u$ back in:
  
  $- e^{- x}$
So, the result is: $e^{- x}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

$$\int \left(- e^{- x}\right)\, dx = C + e^{- x}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

      -1
-1 + e

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

=

      -1
-1 + e

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

-1 + exp(-1)

Numerical answer [src]

-0.632120558828558

-0.632120558828558

The graph

Integral of -e^-x dx

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