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Identical expressions
(x+ two)/ six
(x plus 2) divide by 6
(x plus two) divide by six
x+2/6
(x+2) divide by 6
(x+2)/6dx
Similar expressions
(3x+2)/(6x^2+3x+5)^1/2
(x-2)/6

Solving integrals/ (x+2)/6

Integral of (x+2)/6 dx

The solution

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  3         
  /         
 |          
 |  x + 2   
 |  ----- dx
 |    6     
 |          
/           
1

$$\int\limits_{1}^{3} \frac{x + 2}{6}\, dx$$

Integral((x + 2)/6, (x, 1, 3))

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:
    
    $\int 2\, dx = 2 x$
  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
 |                      
/

$${{{{x^2}\over{2}}+2\,x}\over{6}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

4/3

$${{4}\over{3}}$$

4/3

$$\frac{4}{3}$$

Simplify

Numerical answer [src]

1.33333333333333

1.33333333333333

The graph

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

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Identical expressions

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Integral of (x+2)/6 dx

Limits of integration:

The graph:

Piecewise:

The solution