Mister Exam

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Graphing y =:
(x^2-2)/x
Identical expressions
(x^ two - two)/x
(x squared minus 2) divide by x
(x to the power of two minus two) divide by x
(x2-2)/x
x2-2/x
(x²-2)/x
(x to the power of 2-2)/x
x^2-2/x
(x^2-2) divide by x
(x^2-2)/xdx
Similar expressions
(x^2+2)/x
3*x^2-2/x^3

Solving integrals/ (x^2-2)/x

Integral of (x^2-2)/x dx

The solution

You have entered [src]

  1          
  /          
 |           
 |   2       
 |  x  - 2   
 |  ------ dx
 |    x      
 |           
/            
0

$$\int\limits_{0}^{1} \frac{x^{2} - 2}{x}\, dx$$

Integral((x^2 - 2)/x, (x, 0, 1))

Detail solution

There are multiple ways to do this integral.
Method #1
1. Let $u = x^{2}$ .
  
  Then let $du = 2 x dx$ and substitute $\frac{du}{2}$ :
  
  $\int \frac{u - 2}{2 u}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{u - 2}{u}\, du = \frac{\int \frac{u - 2}{u}\, du}{2}$
    1. Rewrite the integrand:
      
      $\frac{u - 2}{u} = 1 - \frac{2}{u}$
    2. Integrate term-by-term:
      
      The integral of a constant is the constant times the variable of integration:
      
      $\int 1\, du = u$
      
      The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \left(- \frac{2}{u}\right)\, du = - 2 \int \frac{1}{u}\, du$
      
      The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
      
      So, the result is: $- 2 \log{\left(u \right)}$
      
      The result is: $u - 2 \log{\left(u \right)}$
    So, the result is: $\frac{u}{2} - \log{\left(u \right)}$
  Now substitute $u$ back in:
  
  $\frac{x^{2}}{2} - \log{\left(x^{2} \right)}$
Method #2
1. Rewrite the integrand:
  
  $\frac{x^{2} - 2}{x} = x - \frac{2}{x}$
2. 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:
    
    $\int \left(- \frac{2}{x}\right)\, dx = - 2 \int \frac{1}{x}\, dx$
    1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
    So, the result is: $- 2 \log{\left(x \right)}$
  The result is: $\frac{x^{2}}{2} - 2 \log{\left(x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                            
 |                             
 |  2               2          
 | x  - 2          x       / 2\
 | ------ dx = C + -- - log\x /
 |   x             2           
 |                             
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-oo

$$-\infty$$

-oo

$$-\infty$$

-oo

Numerical answer [src]

-87.6808922679858

-87.6808922679858

The graph

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

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Identical expressions

Similar expressions

Integral of (x^2-2)/x dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2