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-x^(2)*e^x

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1          
  /          
 |           
 |    2  x   
 |  -x *e  dx
 |           
/            
0            
$$\int\limits_{0}^{1} - x^{2} e^{x}\, dx$$
Integral((-x^2)*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. 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:

  4. Now simplify:

  5. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                     
 |                                      
 |   2  x             x    2  x        x
 | -x *e  dx = C - 2*e  - x *e  + 2*x*e 
 |                                      
/                                       
$$-\left(x^2-2\,x+2\right)\,e^{x}$$
The graph
The answer [src]
2 - e
$$2-e$$
=
=
2 - e
$$2 - e$$
Numerical answer [src]
-0.718281828459045
-0.718281828459045
The graph
Integral of -x^(2)*e^x dx

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