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4x- one / five - two x-x^2
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4x+1/5-2x-x^2
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Integral of 4x-1/5-2x-x^2 dx

The solution

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  0                          
  /                          
 |                           
 |  /                   2\   
 |  \4*x - 1/5 - 2*x - x / dx
 |                           
/                            
0

$$\int\limits_{0}^{0} \left(- x^{2} + \left(- 2 x + \left(4 x - \frac{1}{5}\right)\right)\right)\, dx$$

Integral(4*x - 1/5 - 2*x - x^2, (x, 0, 0))

Detail solution

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

$x \left(- \frac{x^{2}}{3} + x - \frac{1}{5}\right)$
Add the constant of integration:

$x \left(- \frac{x^{2}}{3} + x - \frac{1}{5}\right)+ \mathrm{constant}$

The answer is:

$x \left(- \frac{x^{2}}{3} + x - \frac{1}{5}\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

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

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Integral of 4x-1/5-2x-x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution