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Identical expressions
6x^ two -6ax-12x
6x squared minus 6ax minus 12x
6x to the power of two minus 6ax minus 12x
6x2-6ax-12x
6x²-6ax-12x
6x to the power of 2-6ax-12x
6x^2-6ax-12xdx
Similar expressions
6x^2+6ax-12x
6x^2-6ax+12x

Integral of 6x^2-6ax-12x dx

The solution

You have entered [src]

  1                         
  /                         
 |                          
 |  /   2               \   
 |  \6*x  - 6*a*x - 12*x/ dx
 |                          
/                           
0

$$\int\limits_{0}^{1} \left(- 12 x + \left(- 6 a x + 6 x^{2}\right)\right)\, dx$$

Integral(6*x^2 - 6*a*x - 12*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:
  
  $\int \left(- 12 x\right)\, dx = - 12 \int x\, dx$
  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: $- 6 x^{2}$
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 6 a x\right)\, dx = - 6 a \int x\, dx$
    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: $- 3 a x^{2}$
  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: $2 x^{3}$
  The result is: $- 3 a x^{2} + 2 x^{3}$
The result is: $- 3 a x^{2} + 2 x^{3} - 6 x^{2}$
Now simplify:

$x^{2} \left(- 3 a + 2 x - 6\right)$
Add the constant of integration:

$x^{2} \left(- 3 a + 2 x - 6\right)+ \mathrm{constant}$

The answer is:

$x^{2} \left(- 3 a + 2 x - 6\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                   
 |                                                    
 | /   2               \             2      3        2
 | \6*x  - 6*a*x - 12*x/ dx = C - 6*x  + 2*x  - 3*a*x 
 |                                                    
/

$$\int \left(- 12 x + \left(- 6 a x + 6 x^{2}\right)\right)\, dx = C - 3 a x^{2} + 2 x^{3} - 6 x^{2}$$

Simplify

The answer [src]

-4 - 3*a

$$- 3 a - 4$$

-4 - 3*a

$$- 3 a - 4$$

-4 - 3*a

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

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Integral of 6x^2-6ax-12x dx

Limits of integration:

The graph:

Piecewise:

The solution