$ \int_a^x \frac {dx} {x^4 - c^4} = \frac {1} {4c^3} \ln \left(\frac {x-c} {x+c} \right)_a^x - \frac {1} {2c^3} \tan^{-1} \Bigl(\frac {x} {c} \Bigr)_a^x $ $ =\frac {1} {4c^3} \Bigl[ \ln \Bigl(\frac {x-c} {x+c} \Bigr) - \ln \Bigl(\frac {a-c} {a+c} \Bigr) \Bigr]- \frac {1} {2c^3} \Bigl[\tan^{-1} \Bigl(\frac {x} {c} \Bigr)-\tan^{-1} \Bigl(\frac {a} {c} \Bigr)\Bigr]$
When $x$ is less than $c$, or when $a$ is less than $c$, the number in the natural log becomes negative. Then, should the general answer have absolute sign instead of parenthesis as below? Is this a more proper or general answer?
$ =\frac {1} {4c^3} \left[ \ln \left|\frac {x-c} {x+c} \right| - \ln \left| \frac {a-c} {a+c} \right| \right] $