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Integral of d{x}:
Integral of x/e^x
Integral of e^(-3x)
Integral of y^2
Integral of xe^(x^2)
Graphing y =:
(x^2-1)/(x^2+1)
Derivative of:
(x^2-1)/(x^2+1)
How do you in partial fractions?:
(x^2-1)/(x^2+1)
Identical expressions
(x^ two - one)/(x^ two + one)
(x squared minus 1) divide by (x squared plus 1)
(x to the power of two minus one) divide by (x to the power of two plus one)
(x2-1)/(x2+1)
x2-1/x2+1
(x²-1)/(x²+1)
(x to the power of 2-1)/(x to the power of 2+1)
x^2-1/x^2+1
(x^2-1) divide by (x^2+1)
(x^2-1)/(x^2+1)dx
Similar expressions
(x^2+1)/(x^2+1)
(x^2-1)/(x^2-1)

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

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

The solution

You have entered [src]

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

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

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

Detail solution

There are multiple ways to do this integral.
Method #1
1. Rewrite the integrand:
  
  $\frac{x^{2} - 1}{x^{2} + 1} = 1 - \frac{2}{x^{2} + 1}$
2. 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:
    
    $\int \left(- \frac{2}{x^{2} + 1}\right)\, dx = - 2 \int \frac{1}{x^{2} + 1}\, dx$
    1. The integral of $\frac{1}{x^{2} + 1}$ is $\operatorname{atan}{\left(x \right)}$ .
    So, the result is: $- 2 \operatorname{atan}{\left(x \right)}$
  The result is: $x - 2 \operatorname{atan}{\left(x \right)}$
Method #2
1. Rewrite the integrand:
  
  $\frac{x^{2} - 1}{x^{2} + 1} = \frac{x^{2}}{x^{2} + 1} - \frac{1}{x^{2} + 1}$
2. Integrate term-by-term:
  1. Rewrite the integrand:
    
    $\frac{x^{2}}{x^{2} + 1} = 1 - \frac{1}{x^{2} + 1}$
  2. 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:
      
      $\int \left(- \frac{1}{x^{2} + 1}\right)\, dx = - \int \frac{1}{x^{2} + 1}\, dx$
      
      The integral of $\frac{1}{x^{2} + 1}$ is $\operatorname{atan}{\left(x \right)}$ .
      
      So, the result is: $- \operatorname{atan}{\left(x \right)}$
    The result is: $x - \operatorname{atan}{\left(x \right)}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- \frac{1}{x^{2} + 1}\right)\, dx = - \int \frac{1}{x^{2} + 1}\, dx$
    1. The integral of $\frac{1}{x^{2} + 1}$ is $\operatorname{atan}{\left(x \right)}$ .
    So, the result is: $- \operatorname{atan}{\left(x \right)}$
  The result is: $x - 2 \operatorname{atan}{\left(x \right)}$
Add the constant of integration:

$x - 2 \operatorname{atan}{\left(x \right)}+ \mathrm{constant}$

The answer is:

$x - 2 \operatorname{atan}{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$x-2\,\arctan x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

    pi
1 - --
    2

$$-{{\pi-2}\over{2}}$$

    pi
1 - --
    2

$$- \frac{\pi}{2} + 1$$

Simplify

Numerical answer [src]

-0.570796326794897

-0.570796326794897

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2