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Identical expressions
one -x-4x^ three +2x^ five
1 minus x minus 4x cubed plus 2x to the power of 5
one minus x minus 4x to the power of three plus 2x to the power of five
1-x-4x3+2x5
1-x-4x³+2x⁵
1-x-4x to the power of 3+2x to the power of 5
1-x-4x^3+2x^5dx
Similar expressions
1-x-4x^3-2x^5
1-x+4x^3+2x^5
1+x-4x^3+2x^5

Solving integrals/ 1-x-4x^3+2x^5

Integral of 1-x-4x^3+2x^5 dx

The solution

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

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

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

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                                               
 |                                          2    6
 | /           3      5\               4   x    x 
 | \1 - x - 4*x  + 2*x / dx = C + x - x  - -- + --
 |                                         2    3 
/

$$\int \left(2 x^{5} - 4 x^{3} - x + 1\right)\, dx = C + \frac{x^{6}}{3} - x^{4} - \frac{x^{2}}{2} + x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$1104$$

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Numerical answer [src]

1104.0

1104.0

The graph

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

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Integral of 1-x-4x^3+2x^5 dx

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Piecewise:

The solution