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Identical expressions
J(4x³+3x²-2x- eight)dx
J(4x³ plus 3x² minus 2x minus 8)dx
J(4x³ plus 3x² minus 2x minus eight)dx
J4x³+3x²-2x-8dx
Similar expressions
J(4x³+3x²-2x+8)dx
J(4x³-3x²-2x-8)dx
J(4x³+3x²+2x-8)dx

Integral of J(4x³+3x²-2x-8)dx dx

The solution

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  1                             
  /                             
 |                              
 |    /   3      2          \   
 |  I*\4*x  + 3*x  - 2*x - 8/ dx
 |                              
/                               
0

$$\int\limits_{0}^{1} i \left(\left(- 2 x + \left(4 x^{3} + 3 x^{2}\right)\right) - 8\right)\, dx$$

Integral(i*(4*x^3 + 3*x^2 - 2*x - 8), (x, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int i \left(\left(- 2 x + \left(4 x^{3} + 3 x^{2}\right)\right) - 8\right)\, dx = i \int \left(\left(- 2 x + \left(4 x^{3} + 3 x^{2}\right)\right) - 8\right)\, dx$
1. 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:
      
      $\int \left(- 2 x\right)\, dx = - 2 \int x\, dx$
      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:
        
        $\int 4 x^{3}\, dx = 4 \int x^{3}\, dx$
        
        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: $x^{4}$
      1. The integral of a constant times a function is the constant times the integral of the function:
        
        $\int 3 x^{2}\, dx = 3 \int x^{2}\, dx$
        
        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: $x^{3}$
      The result is: $x^{4} + x^{3}$
    The result is: $x^{4} + x^{3} - x^{2}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int \left(-8\right)\, dx = - 8 x$
  The result is: $x^{4} + x^{3} - x^{2} - 8 x$
So, the result is: $i \left(x^{4} + x^{3} - x^{2} - 8 x\right)$
Now simplify:

$i x \left(x^{3} + x^{2} - x - 8\right)$
Add the constant of integration:

$i x \left(x^{3} + x^{2} - x - 8\right)+ \mathrm{constant}$

The answer is:

$i x \left(x^{3} + x^{2} - x - 8\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                         
 |                                                          
 |   /   3      2          \            / 3    4    2      \
 | I*\4*x  + 3*x  - 2*x - 8/ dx = C + I*\x  + x  - x  - 8*x/
 |                                                          
/

$$\int i \left(\left(- 2 x + \left(4 x^{3} + 3 x^{2}\right)\right) - 8\right)\, dx = C + i \left(x^{4} + x^{3} - x^{2} - 8 x\right)$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-7*I

$$- 7 i$$

-7*I

$$- 7 i$$

-7*i

Numerical answer [src]

(0.0 - 7.0j)

(0.0 - 7.0j)

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

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Identical expressions

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Integral of J(4x³+3x²-2x-8)dx dx

Limits of integration:

The graph:

Piecewise:

The solution