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x^2e^-x^3
Solving integrals/ x^2e^-x^3

Integral of x^2e^-x^3 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |        3   
 |   2  -x    
 |  x *E    dx
 |            
/             
0
$$\int\limits_{0}^{1} e^{- x^{3}} x^{2}\, dx$$ 
Integral(x^2*E^(-x^3), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

    1. 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. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                     
 |                     3
 |       3           -x 
 |  2  -x           e   
 | x *E    dx = C - ----
 |                   3  
/
$$\int e^{- x^{3}} x^{2}\, dx = C - \frac{e^{- x^{3}}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
     -1
1   e  
- - ---
3    3
$$\frac{1}{3} - \frac{1}{3 e}$$ 
=
= 
     -1
1   e  
- - ---
3    3
$$\frac{1}{3} - \frac{1}{3 e}$$ 
1/3 - exp(-1)/3
Numerical answer [src] 
0.210706852942853
0.210706852942853
The graph
Integral of x^2e^-x^3 dx

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

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