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Integral of d{x}:
Integral of sin(5*x)
Integral of sin^4(x)
Integral of secx
Integral of 9
Identical expressions
4e^(-4x)
4e to the power of ( minus 4x)
4e(-4x)
4e-4x
4e^-4x
4e^(-4x)dx
Similar expressions
4e^(4x)

Solving integrals/ 4e^(-4x)

Integral of 4e^(-4x) dx

The solution

You have entered [src]

 oo           
  /           
 |            
 |     -4*x   
 |  4*E     dx
 |            
/             
0

$$\int\limits_{0}^{\infty} 4 e^{- 4 x}\, dx$$

Integral(4*E^(-4*x), (x, 0, oo))

Detail solution

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

$\int 4 e^{- 4 x}\, dx = 4 \int e^{- 4 x}\, dx$
1. Let $u = - 4 x$ .
  
  Then let $du = - 4 dx$ and substitute $- \frac{du}{4}$ :
  
  $\int \left(- \frac{e^{u}}{4}\right)\, du$
  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: $- \frac{e^{u}}{4}$
  Now substitute $u$ back in:
  
  $- \frac{e^{- 4 x}}{4}$
So, the result is: $- e^{- 4 x}$
Add the constant of integration:

$- e^{- 4 x}+ \mathrm{constant}$

The answer is:

$- e^{- 4 x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                       
 |    -4*x           -4*x
 | 4*E     dx = C - e    
 |                       
/

$$\int 4 e^{- 4 x}\, dx = C - e^{- 4 x}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$1$$

=

$$1$$

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