Is there a rule for integrating $\int f(x)^{g(x)} dx$? When learning integration there are rules for different combinations of functions. For $f(x)\pm g(x)$ you apply linearity, $f(g(x))$ can be handled by substitution rule and $f(x)g(x)$ is integration by parts. But there seems to be nothing for the case where a function is raised to the power of another function.
$$\int f(x)^{g(x)} dx$$
Is there any rule or technique you can apply to the integral above or is it just a dead end?

In the (rare) case where the integral can be calculated, the best way to begin is probably write $f(x)^{g(x)}$ as $e^{g(x) \log(f(x))}$. After that there's no much that can be done in general.
