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Graphing y =:
x^3*x^2
Derivative of:
x^3*x^2
Identical expressions
x^ three *x^ two
x cubed multiply by x squared
x to the power of three multiply by x to the power of two
x3*x2
x³*x²
x to the power of 3*x to the power of 2
x^3x^2
x3x2
x^3*x^2dx

Solving integrals/ x^3*x^2

Integral of x^3*x^2 dx

The solution

You have entered [src]

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

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

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

Detail solution

There are multiple ways to do this integral.
Method #1
1. Let $u = x^{3}$ .
  
  Then let $du = 3 x^{2} dx$ and substitute $\frac{du}{3}$ :
  
  $\int \frac{u}{3}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int u\, du = \frac{\int u\, du}{3}$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int u\, du = \frac{u^{2}}{2}$
    So, the result is: $\frac{u^{2}}{6}$
  Now substitute $u$ back in:
  
  $\frac{x^{6}}{6}$
Method #2
1. Let $u = x^{2}$ .
  
  Then let $du = 2 x dx$ and substitute $\frac{du}{2}$ :
  
  $\int \frac{u^{2}}{2}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int u^{2}\, du = \frac{\int u^{2}\, du}{2}$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int u^{2}\, du = \frac{u^{3}}{3}$
    So, the result is: $\frac{u^{3}}{6}$
  Now substitute $u$ back in:
  
  $\frac{x^{6}}{6}$
Add the constant of integration:

$\frac{x^{6}}{6}+ \mathrm{constant}$

The answer is:

$\frac{x^{6}}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                 
 |                 6
 |  3  2          x 
 | x *x  dx = C + --
 |                6 
/

$$\int x^{2} x^{3}\, dx = C + \frac{x^{6}}{6}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/6

$$\frac{1}{6}$$

=

1/6

$$\frac{1}{6}$$

1/6

Numerical answer [src]

0.166666666666667

0.166666666666667

The graph

Integral of x^3*x^2 dx

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