Integral of x-6/x dx

The solution

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  6           
  /           
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 |  /    6\   
 |  |x - -| dx
 |  \    x/   
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1

$$\int\limits_{1}^{6} \left(x - \frac{6}{x}\right)\, dx$$

Integral(x - 6/x, (x, 1, 6))

Detail solution

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 times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{6}{x}\right)\, dx = - 6 \int \frac{1}{x}\, dx$
  1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
  So, the result is: $- 6 \log{\left(x \right)}$
The result is: $\frac{x^{2}}{2} - 6 \log{\left(x \right)}$
Add the constant of integration:

$\frac{x^{2}}{2} - 6 \log{\left(x \right)}+ \mathrm{constant}$

The answer is:

$\frac{x^{2}}{2} - 6 \log{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                              
 |                   2           
 | /    6\          x            
 | |x - -| dx = C + -- - 6*log(x)
 | \    x/          2            
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/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

35/2 - 6*log(6)

$$\frac{35}{2} - 6 \log{\left(6 \right)}$$

35/2 - 6*log(6)

$$\frac{35}{2} - 6 \log{\left(6 \right)}$$

35/2 - 6*log(6)

Numerical answer [src]

6.74944318463167

6.74944318463167

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

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Integral of x-6/x dx

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The solution