Integral of (x+2)/3 dx

The solution

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  1         
  /         
 |          
 |  x + 2   
 |  ----- dx
 |    3     
 |          
/           
0

$$\int\limits_{0}^{1} \frac{x + 2}{3}\, dx$$

Integral((x + 2)/3, (x, 0, 1))

Detail solution

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

$\int \frac{x + 2}{3}\, dx = \frac{\int \left(x + 2\right)\, dx}{3}$
1. Integrate term-by-term:
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  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: $\frac{x^{2}}{6} + \frac{2 x}{3}$
Now simplify:

$\frac{x \left(x + 4\right)}{6}$
Add the constant of integration:

$\frac{x \left(x + 4\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x + 4\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

5/6

$$\frac{5}{6}$$

5/6

$$\frac{5}{6}$$

5/6

Numerical answer [src]

0.833333333333333

0.833333333333333

The graph

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

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Integral of (x+2)/3 dx

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The solution