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Identical expressions
y=x^ four -4x+6x^ two -4x
y equally x to the power of 4 minus 4x plus 6x squared minus 4x
y equally x to the power of four minus 4x plus 6x to the power of two minus 4x
y=x4-4x+6x2-4x
y=x⁴-4x+6x²-4x
y=x to the power of 4-4x+6x to the power of 2-4x
y=x^4-4x+6x^2-4xdx
Similar expressions
y=x^4-4x-6x^2-4x
y=x^4-4x+6x^2+4x
y=x^4+4x+6x^2-4x

Solving integrals/ y=x^4-4x+6x^2-4x

Integral of y=x^4-4x+6x^2-4x dx

The solution

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  1                           
  /                           
 |                            
 |  / 4            2      \   
 |  \x  - 4*x + 6*x  - 4*x/ dx
 |                            
/                             
0

$$\int\limits_{0}^{1} \left(- 4 x + \left(6 x^{2} + \left(x^{4} - 4 x\right)\right)\right)\, dx$$

Integral(x^4 - 4*x + 6*x^2 - 4*x, (x, 0, 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:
  
  $\int \left(- 4 x\right)\, dx = - 4 \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $- 2 x^{2}$
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 6 x^{2}\, dx = 6 \int x^{2}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{2}\, dx = \frac{x^{3}}{3}$
    So, the result is: $2 x^{3}$
  1. Integrate term-by-term:
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{4}\, dx = \frac{x^{5}}{5}$
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \left(- 4 x\right)\, dx = - 4 \int x\, dx$
      1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
        
        $\int x\, dx = \frac{x^{2}}{2}$
      So, the result is: $- 2 x^{2}$
    The result is: $\frac{x^{5}}{5} - 2 x^{2}$
  The result is: $\frac{x^{5}}{5} + 2 x^{3} - 2 x^{2}$
The result is: $\frac{x^{5}}{5} + 2 x^{3} - 4 x^{2}$
Now simplify:

$\frac{x^{2} \left(x^{3} + 10 x - 20\right)}{5}$
Add the constant of integration:

$\frac{x^{2} \left(x^{3} + 10 x - 20\right)}{5}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(x^{3} + 10 x - 20\right)}{5}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$\int \left(- 4 x + \left(6 x^{2} + \left(x^{4} - 4 x\right)\right)\right)\, dx = C + \frac{x^{5}}{5} + 2 x^{3} - 4 x^{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-9/5

$$- \frac{9}{5}$$

-9/5

$$- \frac{9}{5}$$

-9/5

Numerical answer [src]

-1.8

-1.8

The graph

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

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Identical expressions

Similar expressions

Integral of y=x^4-4x+6x^2-4x dx

Limits of integration:

The graph:

Piecewise:

The solution