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Identical expressions
x^ three *e^(x^ two)*dx
x cubed multiply by e to the power of (x squared ) multiply by dx
x to the power of three multiply by e to the power of (x to the power of two) multiply by dx
x3*e(x2)*dx
x3*ex2*dx
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x to the power of 3*e to the power of (x to the power of 2)*dx
x^3e^(x^2)dx
x3e(x2)dx
x3ex2dx
x^3e^x^2dx
What you mean?
x^3*e^(x^2)*dx
x^((3*e)^(x^2))*dx
x^((3*e)^(x^2))*dx

You entered:

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

What you mean?

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

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

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

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

The solution

You have entered [src]

  1              
  /              
 |               
 |      / 2\     
 |   3  \x /     
 |  x *e    *1 dx
 |               
/                
0

$$\int\limits_{0}^{1} x^{3} e^{x^{2}} \cdot 1\, dx$$

Integral(x^3*E^(x^2)*1, (x, 0, 1))

Detail solution

Use integration by parts:

$\int \operatorname{u} \operatorname{dv} = \operatorname{u}\operatorname{v} - \int \operatorname{v} \operatorname{du}$

Let $u{\left(x \right)} = x^{3}$ and let $\operatorname{dv}{\left(x \right)} = e^{x^{2}}$ .

Then $\operatorname{du}{\left(x \right)} = 3 x^{2}$ .

To find $v{\left(x \right)}$ :
Now evaluate the sub-integral.
The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{3 \sqrt{\pi} x^{2} \operatorname{erfi}{\left(x \right)}}{2}\, dx = \frac{3 \sqrt{\pi} \int x^{2} \operatorname{erfi}{\left(x \right)}\, dx}{2}$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\frac{x^{3} \operatorname{erfi}{\left(x \right)}}{3} - \frac{x^{2} e^{x^{2}}}{3 \sqrt{\pi}} + \frac{e^{x^{2}}}{3 \sqrt{\pi}}$
So, the result is: $\frac{3 \sqrt{\pi} \left(\frac{x^{3} \operatorname{erfi}{\left(x \right)}}{3} - \frac{x^{2} e^{x^{2}}}{3 \sqrt{\pi}} + \frac{e^{x^{2}}}{3 \sqrt{\pi}}\right)}{2}$
Now simplify:

$\frac{\left(x^{2} - 1\right) e^{x^{2}}}{2}$
Add the constant of integration:

$\frac{\left(x^{2} - 1\right) e^{x^{2}}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\left(x^{2} - 1\right) e^{x^{2}}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

                                /  / 2\                      / 2\\                    
                                |  \x /      3            2  \x /|                    
  /                        ____ | e         x *erfi(x)   x *e    |                    
 |                     3*\/ pi *|-------- + ---------- - --------|                    
 |     / 2\                     |    ____       3            ____|     ____  3        
 |  3  \x /                     \3*\/ pi                 3*\/ pi /   \/ pi *x *erfi(x)
 | x *e    *1 dx = C - ------------------------------------------- + -----------------
 |                                          2                                2        
/

$$\int x^{3} e^{x^{2}} \cdot 1\, dx = C + \frac{\sqrt{\pi} x^{3} \operatorname{erfi}{\left(x \right)}}{2} - \frac{3 \sqrt{\pi} \left(\frac{x^{3} \operatorname{erfi}{\left(x \right)}}{3} - \frac{x^{2} e^{x^{2}}}{3 \sqrt{\pi}} + \frac{e^{x^{2}}}{3 \sqrt{\pi}}\right)}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/2

$${{1}\over{2}}$$

1/2

$$\frac{1}{2}$$

Упростить

Numerical answer [src]

0.5

0.5

The graph

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

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What you mean?

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

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The solution

Other calculators

How to use it?

Identical expressions

What you mean?

You entered:

What you mean?

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

Limits of integration:

The graph:

Piecewise:

The solution

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