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x^3*e^(x^2)
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  • Identical expressions

  • x^ three *e^(x^ two)
  • x cubed multiply by e to the power of (x squared )
  • x to the power of three multiply by e to the power of (x to the power of two)
  • x3*e(x2)
  • x3*ex2
  • x³*e^(x²)
  • x to the power of 3*e to the power of (x to the power of 2)
  • x^3e^(x^2)
  • x3e(x2)
  • x3ex2
  • x^3e^x^2
  • x^3*e^(x^2)dx

Integral of x^3*e^(x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1            
  /            
 |             
 |      / 2\   
 |   3  \x /   
 |  x *E     dx
 |             
/              
0              
$$\int\limits_{0}^{1} e^{x^{2}} x^{3}\, dx$$
Integral(x^3*E^(x^2), (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. 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. 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]
  /                                  
 |                    / 2\       / 2\
 |     / 2\           \x /    2  \x /
 |  3  \x /          e       x *e    
 | x *E     dx = C - ----- + --------
 |                     2        2    
/                                    
$$\int e^{x^{2}} x^{3}\, dx = C + \frac{x^{2} e^{x^{2}}}{2} - \frac{e^{x^{2}}}{2}$$
The graph
The answer [src]
1/2
$$\frac{1}{2}$$
=
=
1/2
$$\frac{1}{2}$$
1/2
Numerical answer [src]
0.5
0.5
The graph
Integral of x^3*e^(x^2) dx

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