Question

Find the integral of x^2/(x^2-1) dx.

Answer 1

use polynomial division to simplify

__1 R 1______
x^2 - 1 | x^2
-( x^2 -1)
--------------
1

\[\int\limits 1 + \frac{1}{x^2 - 1}\]
use partial fractions

Answer 2

I get it. Thanks for the help.

Answer 3

\[\frac{1}{(x-1)(x+1)} = \frac{A}{x-1} + \frac{B}{x+1}\]
\[A + B = 0\]
\[A -B = 1\]
\[A = \frac{1}{2} , B = -\frac{1}{2}\]
\[\int\limits dx +\frac{1}{2}\int\limits \frac{dx}{x-1} -\frac{1}{2}\int\limits \frac{dx}{x+1}\]