Integral of 1/3x-5 dx

The solution

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  1           
  /           
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 |  /x    \   
 |  |- - 5| dx
 |  \3    /   
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0

$$\int\limits_{0}^{1} \left(\frac{x}{3} - 5\right)\, dx$$

Integral(x/3 - 5, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{x}{3}\, dx = \frac{\int x\, dx}{3}$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $\frac{x^{2}}{6}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-5\right)\, dx = - 5 x$
The result is: $\frac{x^{2}}{6} - 5 x$
Now simplify:

$\frac{x \left(x - 30\right)}{6}$
Add the constant of integration:

$\frac{x \left(x - 30\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x - 30\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                         
 |                         2
 | /x    \                x 
 | |- - 5| dx = C - 5*x + --
 | \3    /                6 
 |                          
/

$$\int \left(\frac{x}{3} - 5\right)\, dx = C + \frac{x^{2}}{6} - 5 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-29/6

$$- \frac{29}{6}$$

-29/6

$$- \frac{29}{6}$$

-29/6

Numerical answer [src]

-4.83333333333333

-4.83333333333333

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

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Integral of 1/3x-5 dx

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