Find: \int \frac{e^x dx}{(e^x - 1)^2 (e^x + 2)}

Let us consider $e^x = t$.
We get $e^x dx = dt$.
So we have
$\int \frac{e^x dx}{(e^x - 1)^2 (e^x + 2)} = \int \frac{dt}{t^2 (t + 3)} = \frac{1}{9} \int \frac{1}{t + 3} dt + \frac{1}{9} \int \frac{-t + 3}{t^2} dt = \frac{ln(t + 3)}{9} + \frac{1}{9} (-ln t - \frac{3}{t}) = \frac{ln(t + 3) - ln t - \frac{3}{t}}{9}$