Find all parameters $\alpha \in \mathbb{R} $ such that $\int_{-1}^{0} \frac{2^{x+1} - 3^{x+1}}{\ln(\sin^{\alpha}(x+1)+1)} dx$ converges.

Question

Find all parameters $\alpha \in \mathbb{R} $ such that $$ \int_{-1}^{0} \frac{2^{x+1} - 3^{x+1}}{\ln(\sin^{\alpha}(x+1)+1)} dx$$ converges.

So I take an obvious substitution $t = x + 1$ which gives $$\int_{0}^{1} \frac{2^{t} - 3^{t}}{\ln(\sin^{\alpha}(t)+1)} dt.$$ If I remember correctly with $t \rightarrow 0$, $\ln(\sin^{\alpha}(t)+1) \sim \sin^{\alpha}(t) \sim t^{\alpha}$. How do I find parameters now?