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x^2*e^(x^2)

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x^2*e^(x^2)

What you mean?

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

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1            
  /            
 |             
 |      / 2\   
 |   2  \x /   
 |  x *e     dx
 |             
/              
0              
$$\int\limits_{0}^{1} x^{2} e^{x^{2}}\, dx$$
Integral(x^2*E^(x^2), (x, 0, 1))
Detail solution
  1. Use integration by parts:

    Let and let .

    Then .

    To find :

      ErfRule(a=1, b=0, c=0, context=exp(x**2), symbol=x)

    Now evaluate the sub-integral.

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

    1. Don't know the steps in finding this integral.

      But the integral is

    So, the result is:

  3. Now simplify:

  4. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                                              
 |                          /                          / 2\ \                    
 |     / 2\                 |           2              \x / |     ____  2        
 |  2  \x /            ____ |erfi(x)   x *erfi(x)   x*e     |   \/ pi *x *erfi(x)
 | x *e     dx = C - \/ pi *|------- + ---------- - --------| + -----------------
 |                          |   4          2            ____|           2        
/                           \                       2*\/ pi /                    
$${{\sqrt{\pi}\,i\,\mathrm{erf}\left(i\,x\right)}\over{4}}+{{x\,e^{x^ 2}}\over{2}}$$
The graph
The answer [src]
      ____        
e   \/ pi *erfi(1)
- - --------------
2         4       
$${{\sqrt{\pi}\,i\,\mathrm{erf}\left(i\right)+2\,e}\over{4}}$$
=
=
      ____        
e   \/ pi *erfi(1)
- - --------------
2         4       
$$- \frac{\sqrt{\pi} \operatorname{erfi}{\left(1 \right)}}{4} + \frac{e}{2}$$
Numerical answer [src]
0.627815041275932
0.627815041275932
The graph
Integral of x^2*e^(x^2) dx

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