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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           
$$\int\limits_{0}^{1} x^{3} e^{x}\, dx$$
Integral(x^3*E^x, (x, 0, 1))
Detail solution
  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:

  5. Now simplify:

  6. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                              
 |                                               
 |  3  x             x    3  x      2  x        x
 | x *e  dx = C - 6*e  + x *e  - 3*x *e  + 6*x*e 
 |                                               
/                                                
$$\left(x^3-3\,x^2+6\,x-6\right)\,e^{x}$$
The graph
The answer [src]
6 - 2*e
$$6-2\,e$$
=
=
6 - 2*e
$$6 - 2 e$$
Numerical answer [src]
0.563436343081909
0.563436343081909
The graph
Integral of (x^3)(e^x) dx

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