Let $\gamma ,\mu > 0$ be positive real constants and $\beta \in \mathbb{R}$ be a real constant. How can I evaluate the following indefinite integral?
$$ \int \frac{e^{2\gamma t} (e^{-\mu t} - e^{2\gamma t})}{\beta e^{4 \gamma t}-3 e^{2 \gamma t}+6 e^{\gamma t}-4} \mathrm{d}t $$
If we were dealing only with $e^{\gamma t}$ terms, we could proceed quite easily by substitution ($u = e^{\gamma t}$), but that strategy seems to be foiled by the presence of the $e^{-\mu t}$ term.