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Integral of d{x}:
Integral of sin(5x)
Integral of -e^(-2x)
Integral of xe^(x²+1)
Integral of xe^(2x)dx/(1+2x)^2
Derivative of:
-e^(-2x)
Identical expressions
-e^(-2x)
minus e to the power of ( minus 2x)
-e(-2x)
-e-2x
-e^-2x
-e^(-2x)dx
Similar expressions
-e^(2x)
e^(-2x)

Solving integrals/ -e^(-2x)

Integral of -e^(-2x) dx

The solution

You have entered [src]

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

$$\int\limits_{0}^{1} \left(- e^{- 2 x}\right)\, dx$$

Integral(-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:

$\int \left(- e^{- 2 x}\right)\, dx = - \int e^{- 2 x}\, dx$
1. Let $u = - 2 x$ .
  
  Then let $du = - 2 dx$ and substitute $- \frac{du}{2}$ :
  
  $\int \left(- \frac{e^{u}}{2}\right)\, du$
  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: $- \frac{e^{u}}{2}$
  Now substitute $u$ back in:
  
  $- \frac{e^{- 2 x}}{2}$
So, the result is: $\frac{e^{- 2 x}}{2}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

$$\int \left(- e^{- 2 x}\right)\, dx = C + \frac{e^{- 2 x}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

       -2
  1   e  
- - + ---
  2    2

$$- \frac{1}{2} + \frac{1}{2 e^{2}}$$

=

       -2
  1   e  
- - + ---
  2    2

$$- \frac{1}{2} + \frac{1}{2 e^{2}}$$

-1/2 + exp(-2)/2

Numerical answer [src]

-0.432332358381694

-0.432332358381694

The graph

Integral of -e^(-2x) dx

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