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Identical expressions
x^ two *exp(x^ three)
x squared multiply by exponent of (x cubed )
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x2*exp(x3)
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x to the power of 2*exp(x to the power of 3)
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x^2expx^3
x^2*exp(x^3)dx

Solving integrals/ x^2*exp(x^3)

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

The solution

You have entered [src]

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

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

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

Detail solution

Let $u = x^{3}$ .

Then let $du = 3 x^{2} dx$ and substitute $\frac{du}{3}$ :

$\int \frac{e^{u}}{3}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\text{False}$
  1. The integral of the exponential function is itself.
    
    $\int e^{u}\, du = e^{u}$
  So, the result is: $\frac{e^{u}}{3}$
Now substitute $u$ back in:

$\frac{e^{x^{3}}}{3}$
Add the constant of integration:

$\frac{e^{x^{3}}}{3}+ \mathrm{constant}$

The answer is:

$\frac{e^{x^{3}}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                       
 |                    / 3\
 |     / 3\           \x /
 |  2  \x /          e    
 | x *e     dx = C + -----
 |                     3  
/

$$\int x^{2} e^{x^{3}}\, dx = C + \frac{e^{x^{3}}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  1   E
- - + -
  3   3

$$- \frac{1}{3} + \frac{e}{3}$$

  1   E
- - + -
  3   3

$$- \frac{1}{3} + \frac{e}{3}$$

-1/3 + E/3

Numerical answer [src]

0.572760609486348

0.572760609486348

The graph

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

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Identical expressions

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

Limits of integration:

The graph:

Piecewise:

The solution