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Identical expressions
с*(absx+ one / two)
с multiply by (absx plus 1 divide by 2)
с multiply by (absx plus one divide by two)
с(absx+1/2)
сabsx+1/2
с*(absx+1 divide by 2)
с*(absx+1/2)dx
Similar expressions
с*(absx-1/2)

Integral of с*(absx+1/2) dx

The solution

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  5/4                
   /                 
  |                  
  |  c*(|x| + 1/2) dx
  |                  
 /                   
-5/4

$$\int\limits_{- \frac{5}{4}}^{\frac{5}{4}} c \left(\left|{x}\right| + \frac{1}{2}\right)\, dx$$

Integral(c*(|x| + 1/2), (x, -5/4, 5/4))

Detail solution

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

$\int c \left(\left|{x}\right| + \frac{1}{2}\right)\, dx = c \int \left(\left|{x}\right| + \frac{1}{2}\right)\, dx$
1. Integrate term-by-term:
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $\int \left|{x}\right|\, dx$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int \frac{1}{2}\, dx = \frac{x}{2}$
  The result is: $\frac{x}{2} + \int \left|{x}\right|\, dx$
So, the result is: $c \left(\frac{x}{2} + \int \left|{x}\right|\, dx\right)$
Now simplify:

$\frac{c \left(x + 2 \int \left|{x}\right|\, dx\right)}{2}$
Add the constant of integration:

$\frac{c \left(x + 2 \int \left|{x}\right|\, dx\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{c \left(x + 2 \int \left|{x}\right|\, dx\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                         /      /      \
 |                          |x    |       |
 | c*(|x| + 1/2) dx = C + c*|- +  | |x| dx|
 |                          |2    |       |
/                           \    /        /

$$\int c \left(\left|{x}\right| + \frac{1}{2}\right)\, dx = C + c \left(\frac{x}{2} + \int \left|{x}\right|\, dx\right)$$

Simplify

The answer [src]

45*c
----
 16

$$\frac{45 c}{16}$$

45*c
----
 16

$$\frac{45 c}{16}$$

45*c/16

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

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Integral of с*(absx+1/2) dx

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The solution