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

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

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

The solution

You have entered [src]

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

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

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

Detail solution

Rewrite the integrand:

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

$x + \frac{\log{\left(x - 1 \right)}}{2} - \frac{\log{\left(x + 1 \right)}}{2}+ \mathrm{constant}$

The answer is:

$x + \frac{\log{\left(x - 1 \right)}}{2} - \frac{\log{\left(x + 1 \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

      pi*I
-oo - ----
       2

$$-\infty - \frac{i \pi}{2}$$

      pi*I
-oo - ----
       2

$$-\infty - \frac{i \pi}{2}$$

-oo - pi*i/2

Numerical answer [src]

-21.3920519833869

-21.3920519833869

The graph

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

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Identical expressions

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

Limits of integration:

The graph:

Piecewise:

The solution