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Identical expressions
e^(x*(- two))*dx
e to the power of (x multiply by ( minus 2)) multiply by dx
e to the power of (x multiply by ( minus two)) multiply by dx
e(x*(-2))*dx
ex*-2*dx
e^(x(-2))dx
e(x(-2))dx
ex-2dx
e^x-2dx
Similar expressions
e^(x*(2))*dx

Solving integrals/ e^(x*(-2))*dx

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

The solution

You have entered [src]

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

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

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

Detail solution

Let $u = \left(-2\right) x$ .

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:

$- \frac{e^{\left(-2\right) x}}{2}$
Now simplify:

$- \frac{e^{- 2 x}}{2}$
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]

  /                        
 |                   x*(-2)
 |  x*(-2)          e      
 | E       dx = C - -------
 |                     2   
/

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

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