I'm wondering whether any of these two indefinite integrals
$$\int \frac{1}{\sqrt{1+\alpha \sinh(x)^{-4/3}}}dx$$ $$\int \frac{\sinh(x)^{-4/3}}{\sqrt{1+\alpha\sinh(x)^{-4/3}}}dx$$
can be evaluated in closed form. I've tried a couple of substitutions, looked at integral tables, and asked Mathematica, to no avail so far.