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Identical expressions
two x^ three *x^2
2x cubed multiply by x squared
two x to the power of three multiply by x squared
2x3*x2
2x³*x²
2x to the power of 3*x to the power of 2
2x^3x^2
2x3x2
2x^3*x^2dx
What you mean?
2*x^3*x^2
2*x^((3*x)^2)
2*x^((3*x)^2)

Solving integrals/ 2x^3*x^2

You entered:

2x^3*x^2

What you mean?

2*x^3*x^2

2*x^((3*x)^2)

2*x^((3*x)^2)

Integral of 2x^3*x^2 dx

The solution

You have entered [src]

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

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

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

Detail solution

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

$\int 2 x^{2} x^{3}\, dx = 2 \int x^{2} x^{3}\, dx$
1. There are multiple ways to do this integral.
  Method #1
  1. Let $u = x^{2}$ .
    
    Then let $du = 2 x dx$ and substitute $\frac{du}{2}$ :
    
    $\int \frac{u^{2}}{4}\, du$
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \frac{u^{2}}{2}\, du = \frac{\int u^{2}\, du}{2}$
      
      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:
    
    $\frac{x^{6}}{6}$
  Method #2
  1. Let $u = x^{3}$ .
    
    Then let $du = 3 x^{2} dx$ and substitute $\frac{du}{3}$ :
    
    $\int \frac{u}{9}\, du$
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \frac{u}{3}\, du = \frac{\int u\, du}{3}$
      
      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:
    
    $\frac{x^{6}}{6}$
So, the result is: $\frac{x^{6}}{3}$
Add the constant of integration:

$\frac{x^{6}}{3}+ \mathrm{constant}$

The answer is:

$\frac{x^{6}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$${{x^6}\over{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/3

$${{1}\over{3}}$$

=

1/3

$$\frac{1}{3}$$

Упростить

Numerical answer [src]

0.333333333333333

0.333333333333333

The graph

Integral of 2x^3*x^2 dx

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