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

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

The solution

You have entered [src]

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

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

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

Detail solution

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

$x \left(\frac{x^{4}}{5} - \frac{x^{3}}{2} - x^{2} + 2 x + 4\right)$
Add the constant of integration:

$x \left(\frac{x^{4}}{5} - \frac{x^{3}}{2} - x^{2} + 2 x + 4\right)+ \mathrm{constant}$

The answer is:

$x \left(\frac{x^{4}}{5} - \frac{x^{3}}{2} - x^{2} + 2 x + 4\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

81
--
10

$$\frac{81}{10}$$

81
--
10

$$\frac{81}{10}$$

81/10

Numerical answer [src]

8.1

8.1

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

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

Limits of integration:

The graph:

Piecewise:

The solution