Fastest way to integrate $\frac{1}{t(t^6-1)}$ My friend mentioned to me that there is a very quick way to integrate $\frac{1}{t(t^6-1)}$. 
The standard method for dealing with integrals of rational functions by partial fraction decomposition is long (but doable) as there are 5 terms to integrate. After playing around for some time I still don't see the fast way of doing this integral.
Am I missing something obvious?

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\begin{align}
\int{\dd t \over t\pars{t^{6} - 1}} &
\,\,\,\stackrel{t\ =\ x^{-2}}{=}\,\,\,
2\int{x^{11} \over x^{12} - 1}\,\dd x = {1 \over 6}\,\ln\pars{x^{12} - 1} =
{1 \over 6}\,\ln\pars{{1 \over t^{6}} - 1}
\\[5mm] & =
\bbx{\ds{{1 \over 6}\,\ln\pars{1 - t^{6}} - \ln\pars{t} +
\pars{~\mbox{a constant}~}}}
\end{align}
