The value of the definite integral $\int_0^{\pi}\dfrac{1}{5 + 4\cos x}\, dx$ is equal to ...

Let $f(x) = x - [x]$ for every real number $x$, where $[x]$ is integral part of $x$. then $\int\limits_{-1}^{1} f(x)\, dx$ is

The value of $\int_0^\pi \dfrac{1}{1 + 2^{\cos x}}\,dx$ is _____

If $I_n = \int_1^e (\log_e x)^n\,dx$ where $n \in Z^+$ and $I_m + mI_{2026} = e$, then $m = $