I want to integrate
\[\frac{x^2}{1-x^2},\]
what I have try is trigonometric substitution and partition function and integration by part
but still cannot solve it
Thx for your reading!
I want to integrate
\[\frac{x^2}{1-x^2},\]
what I have try is trigonometric substitution and partition function and integration by part
but still cannot solve it
Thx for your reading!
$\frac{x^2}{1-x^2} = -\frac{x^2}{x^2 - 1} = -\frac{x^2 - 1 + 1}{x^2 - 1} = -1 - \frac{1}{x^2 - 1}$ Can you take it from here?
And going a little further,
$\frac{1}{x^2-1} = \frac{1}{(x-1)(x+1)} =\frac{1}{2}\left(\frac{1}{x-1}-\frac{1}{x+1}\right) $
At this point, even I can integrate it.