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Identical expressions
x^ two -2x^ three -2x^ five + four x^4
x squared minus 2x cubed minus 2x to the power of 5 plus 4x to the power of 4
x to the power of two minus 2x to the power of three minus 2x to the power of five plus four x to the power of 4
x2-2x3-2x5+4x4
x²-2x³-2x⁵+4x⁴
x to the power of 2-2x to the power of 3-2x to the power of 5+4x to the power of 4
x^2-2x^3-2x^5+4x^4dx
Similar expressions
x^2+2x^3-2x^5+4x^4
x^2-2x^3+2x^5+4x^4
x^2-2x^3-2x^5-4x^4

Solving integrals/ x^2-2x^3-2x^5+4x^4

Integral of x^2-2x^3-2x^5+4x^4 dx

The solution

You have entered [src]

  1                             
  /                             
 |                              
 |  / 2      3      5      4\   
 |  \x  - 2*x  - 2*x  + 4*x / dx
 |                              
/                               
-1

$$\int\limits_{-1}^{1} \left(- 2 x^{5} + 4 x^{4} - 2 x^{3} + x^{2}\right)\, dx$$

Integral(x^2 - 2*x^3 - 2*x^5 + 4*x^4, (x, -1, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 2 x^{5}\right)\, dx = - \int 2 x^{5}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 2 x^{5}\, dx = 2 \int x^{5}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{5}\, dx = \frac{x^{6}}{6}$
    So, the result is: $\frac{x^{6}}{3}$
  So, the result is: $- \frac{x^{6}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 4 x^{4}\, dx = 4 \int x^{4}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{4}\, dx = \frac{x^{5}}{5}$
  So, the result is: $\frac{4 x^{5}}{5}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 2 x^{3}\right)\, dx = - \int 2 x^{3}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 2 x^{3}\, dx = 2 \int x^{3}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{3}\, dx = \frac{x^{4}}{4}$
    So, the result is: $\frac{x^{4}}{2}$
  So, the result is: $- \frac{x^{4}}{2}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
The result is: $- \frac{x^{6}}{3} + \frac{4 x^{5}}{5} - \frac{x^{4}}{2} + \frac{x^{3}}{3}$
Now simplify:

$\frac{x^{3} \left(- 10 x^{3} + 24 x^{2} - 15 x + 10\right)}{30}$
Add the constant of integration:

$\frac{x^{3} \left(- 10 x^{3} + 24 x^{2} - 15 x + 10\right)}{30}+ \mathrm{constant}$

The answer is:

$\frac{x^{3} \left(- 10 x^{3} + 24 x^{2} - 15 x + 10\right)}{30}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                      
 |                                     4    6    3      5
 | / 2      3      5      4\          x    x    x    4*x 
 | \x  - 2*x  - 2*x  + 4*x / dx = C - -- - -- + -- + ----
 |                                    2    3    3     5  
/

$$-{{x^6}\over{3}}+{{4\,x^5}\over{5}}-{{x^4}\over{2}}+{{x^3}\over{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

34
--
15

$${{34}\over{15}}$$

34
--
15

$$\frac{34}{15}$$

Упростить

Numerical answer [src]

2.26666666666667

2.26666666666667

The graph

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

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Integral of x^2-2x^3-2x^5+4x^4 dx

Limits of integration:

The graph:

Piecewise:

The solution