Integral of x-(1/x) dx

The solution

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

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

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

$$\int \left(x - \frac{1}{x}\right)\, dx = C + \frac{x^{2}}{2} - \log{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

4 - log(3)

$$4 - \log{\left(3 \right)}$$

4 - log(3)

$$4 - \log{\left(3 \right)}$$

4 - log(3)

Numerical answer [src]

2.90138771133189

2.90138771133189

The graph

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

Other calculators

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Identical expressions

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Integral of x-(1/x) dx

Limits of integration:

The graph:

Piecewise:

The solution