Mister Exam

Other calculators

Integral of (x²+1)/(x²-1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

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)/(x^2 - 1*1), (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      1. The integral of a constant is the constant times the variable of integration:

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. Let .

          Then let and substitute :

          1. The integral of is .

          Now substitute back in:

        So, the result is:

      1. Let .

        Then let and substitute :

        1. The integral of is .

        Now substitute back in:

      The result is:

    Method #2

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      1. Rewrite the integrand:

      2. Integrate term-by-term:

        1. The integral of a constant is the constant times the variable of integration:

        1. The integral of a constant times a function is the constant times the integral of the function:

          1. Let .

            Then let and substitute :

            1. The integral of is .

            Now substitute back in:

          So, the result is:

        1. The integral of a constant times a function is the constant times the integral of the function:

          1. Let .

            Then let and substitute :

            1. The integral of is .

            Now substitute back in:

          So, the result is:

        The result is:

      1. Rewrite the integrand:

      2. The integral of a constant times a function is the constant times the integral of the function:

        1. Integrate term-by-term:

          1. The integral of is .

          1. The integral of a constant times a function is the constant times the integral of the function:

            1. The integral of is .

            So, the result is:

          The result is:

        So, the result is:

      The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                            
 |                                             
 |  2                                          
 | x  + 1                                      
 | ------ dx = C + x - log(1 + x) + log(-1 + x)
 |  2                                          
 | x  - 1                                      
 |                                             
/                                              
$$-\log \left(x+1\right)+x+\log \left(x-1\right)$$
The answer [src]
-oo - pi*I
$${\it \%a}$$
=
=
-oo - pi*I
$$-\infty - i \pi$$
Numerical answer [src]
-43.7841039667738
-43.7841039667738

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