Integral of (x+3)/2 dx

The solution

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  3         
  /         
 |          
 |  x + 3   
 |  ----- dx
 |    2     
 |          
/           
9

$$\int\limits_{9}^{3} \frac{x + 3}{2}\, dx$$

Integral((x + 3)/2, (x, 9, 3))

Detail solution

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

$\int \frac{x + 3}{2}\, dx = \frac{\int \left(x + 3\right)\, dx}{2}$
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: $\frac{x^{2}}{4} + \frac{3 x}{2}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                       
 |                 2      
 | x + 3          x    3*x
 | ----- dx = C + -- + ---
 |   2            4     2 
 |                        
/

$$\int \frac{x + 3}{2}\, dx = C + \frac{x^{2}}{4} + \frac{3 x}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-27

$$-27$$

-27

$$-27$$

-27

Numerical answer [src]

-27.0

-27.0

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

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Integral of (x+3)/2 dx

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The solution