Integral of (x+3)/3 dx

The solution

You have entered [src]

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

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

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

Detail solution

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

$\int \frac{x + 3}{3}\, dx = \frac{\int \left(x + 3\right)\, dx}{3}$
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:
    
    $\int 3\, dx = 3 x$
  The result is: $\frac{x^{2}}{2} + 3 x$
So, the result is: $\frac{x^{2}}{6} + x$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

7/6

$$\frac{7}{6}$$

7/6

$$\frac{7}{6}$$

7/6

Numerical answer [src]

1.16666666666667

1.16666666666667

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (x+3)/3 dx

Limits of integration:

The graph:

Piecewise:

The solution