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Graphing y =:
(x^2-1)/x
Derivative of:
(x^2-1)/x
Identical expressions
(x^ two - one)/x
(x squared minus 1) divide by x
(x to the power of two minus one) divide by x
(x2-1)/x
x2-1/x
(x²-1)/x
(x to the power of 2-1)/x
x^2-1/x
(x^2-1) divide by x
(x^2-1)/xdx
Similar expressions
(x^2-(1/x)^2)п
(x^2-1)/(x^3+x)
(x^5+2*x^2-1)/x^4
(x^2+1)/x

Solving integrals/ (x^2-1)/x

Integral of (x^2-1)/x dx

The solution

You have entered [src]

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

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

Integral((x^2 - 1)/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 $\frac{du}{2}$ :
  
  $\int \frac{u - 1}{2 u}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{u - 1}{u}\, du = \frac{\int \frac{u - 1}{u}\, du}{2}$
    1. Rewrite the integrand:
      
      $\frac{u - 1}{u} = 1 - \frac{1}{u}$
    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:
      
      $\int \left(- \frac{1}{u}\right)\, du = - \int \frac{1}{u}\, du$
      
      The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
      
      So, the result is: $- \log{\left(u \right)}$
      
      The result is: $u - \log{\left(u \right)}$
    So, the result is: $\frac{u}{2} - \frac{\log{\left(u \right)}}{2}$
  Now substitute $u$ back in:
  
  $\frac{x^{2}}{2} - \frac{\log{\left(x^{2} \right)}}{2}$
Method #2
1. Rewrite the integrand:
  
  $\frac{x^{2} - 1}{x} = x - \frac{1}{x}$
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:
    
    $\int \left(- \frac{1}{x}\right)\, dx = - \int \frac{1}{x}\, dx$
    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:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-oo

$$-\infty$$

-oo

$$-\infty$$

-oo

Numerical answer [src]

-43.5904461339929

-43.5904461339929

The graph

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

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Identical expressions

Similar expressions

Integral of (x^2-1)/x dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2