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Integral of d{x}:
Integral of 1/(x²+1)
Integral of x^5dx
Integral of sin^3x/cosx
Integral of x/sin^2(x)
Identical expressions
2e^(-3x)
2e to the power of ( minus 3x)
2e(-3x)
2e-3x
2e^-3x
2e^(-3x)dx
Similar expressions
2e^(3x)

Solving integrals/ 2e^(-3x)

Integral of 2e^(-3x) dx

The solution

You have entered [src]

 oo           
  /           
 |            
 |     -3*x   
 |  2*E     dx
 |            
/             
2

$$\int\limits_{2}^{\infty} 2 e^{- 3 x}\, dx$$

Integral(2*E^(-3*x), (x, 2, oo))

Detail solution

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

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

$- \frac{2 e^{- 3 x}}{3}+ \mathrm{constant}$

The answer is:

$- \frac{2 e^{- 3 x}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$\int 2 e^{- 3 x}\, dx = C - \frac{2 e^{- 3 x}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

   -6
2*e  
-----
  3

$$\frac{2}{3 e^{6}}$$

=

   -6
2*e  
-----
  3

$$\frac{2}{3 e^{6}}$$

2*exp(-6)/3

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