Question

Evaluate:

$\int \frac{dx}{x^4-1}$.

Answer 1

$\int \frac{dx}{(x^4-1)}$

$=\int \frac{dx}{(x^2+1)(x^2-1)}$

$=\frac{1}{2}|\frac{dx}{x^2-1}-\frac{1}{2}|\frac{dx}{x^2+1}$

$=\frac{1}{4}log\left|\frac{x-1}{x+1}\right|-\frac{1}{2}{\tan }^{-1}\left(\frac{x}{1}\right)+c$

$=\frac{1}{4}log\left|\frac{x-1}{x+1}\right|-\frac{1}{2}{\tan }^{-1}\left(x\right)+c$

[where 'c' is integration constant].