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(one / six)*(x- two)
(1 divide by 6) multiply by (x minus 2)
(one divide by six) multiply by (x minus two)
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(1 divide by 6)*(x-2)
(1/6)*(x-2)dx
Similar expressions
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Integral of (1/6)*(x-2) dx

The solution

You have entered [src]

  x         
  /         
 |          
 |  x - 2   
 |  ----- dx
 |    6     
 |          
/           
1

$$\int\limits_{1}^{x} \frac{x - 2}{6}\, dx$$

Integral((x - 2)/6, (x, 1, x))

Detail solution

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

$\int \frac{x - 2}{6}\, dx = \frac{\int \left(x - 2\right)\, dx}{6}$
1. Integrate term-by-term:
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int \left(-2\right)\, dx = - 2 x$
  The result is: $\frac{x^{2}}{2} - 2 x$
So, the result is: $\frac{x^{2}}{12} - \frac{x}{3}$
Now simplify:

$\frac{x \left(x - 4\right)}{12}$
Add the constant of integration:

$\frac{x \left(x - 4\right)}{12}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x - 4\right)}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$\int \frac{x - 2}{6}\, dx = C + \frac{x^{2}}{12} - \frac{x}{3}$$

Simplify

The answer [src]

$$\frac{x^{2}}{12} - \frac{x}{3} + \frac{1}{4}$$

$$\frac{x^{2}}{12} - \frac{x}{3} + \frac{1}{4}$$

1/4 - x/3 + x^2/12

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

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Integral of (1/6)*(x-2) dx

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The solution