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Solving integrals/ (x+3)/2

Integral of (x+3)/2 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  3         
  /         
 |          
 |  x + 3   
 |  ----- dx
 |    2     
 |          
/           
9
∫93x+32 dx\int\limits_{9}^{3} \frac{x + 3}{2}\, dx 
Integral((x + 3)/2, (x, 9, 3))
Detail solution

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

    ∫x+32 dx=∫(x+3) dx2\int \frac{x + 3}{2}\, dx = \frac{\int \left(x + 3\right)\, dx}{2}

    1. Integrate term-by-term:

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

      1. The integral of a constant is the constant times the variable of integration:

        ∫3 dx=3x\int 3\, dx = 3 x

      The result is: x22+3x\frac{x^{2}}{2} + 3 x

    So, the result is: x24+3x2\frac{x^{2}}{4} + \frac{3 x}{2}

  2. Now simplify:

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

  3. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                       
 |                 2      
 | x + 3          x    3*x
 | ----- dx = C + -- + ---
 |   2            4     2 
 |                        
/
∫x+32 dx=C+x24+3x2\int \frac{x + 3}{2}\, dx = C + \frac{x^{2}}{4} + \frac{3 x}{2}
Simplify
The graph
3.09.03.54.04.55.05.56.06.57.07.58.08.5050
Plot the graph f(x)
The answer [src] 
-27
−27-27 
=
= 
-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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