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x^3*e^(-x)

Integral of x^3*e^(-x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1          
  /          
 |           
 |   3  -x   
 |  x *E   dx
 |           
/            
0            
$$\int\limits_{0}^{1} e^{- x} x^{3}\, dx$$
Integral(x^3*E^(-x), (x, 0, 1))
Detail solution
  1. Let .

    Then let and substitute :

    1. Use integration by parts:

      Let and let .

      Then .

      To find :

      1. The integral of the exponential function is itself.

      Now evaluate the sub-integral.

    2. Use integration by parts:

      Let and let .

      Then .

      To find :

      1. The integral of the exponential function is itself.

      Now evaluate the sub-integral.

    3. Use integration by parts:

      Let and let .

      Then .

      To find :

      1. The integral of the exponential function is itself.

      Now evaluate the sub-integral.

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

      1. The integral of the exponential function is itself.

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                   
 |                                                    
 |  3  -x             -x    3  -x        -x      2  -x
 | x *E   dx = C - 6*e   - x *e   - 6*x*e   - 3*x *e  
 |                                                    
/                                                     
$$\int e^{- x} x^{3}\, dx = C - x^{3} e^{- x} - 3 x^{2} e^{- x} - 6 x e^{- x} - 6 e^{- x}$$
The graph
The answer [src]
        -1
6 - 16*e  
$$6 - \frac{16}{e}$$
=
=
        -1
6 - 16*e  
$$6 - \frac{16}{e}$$
6 - 16*exp(-1)
Numerical answer [src]
0.113928941256923
0.113928941256923
The graph
Integral of x^3*e^(-x) dx

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