$\int x^3 \log x\,dx = $

If $f'(x) = \dfrac{(\sqrt{x}+1)e^{\sqrt{x}}}{\sqrt{x}}$ and $f(0) = e$ then $f(1) = \ldots\ldots\ldots\ldots$

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 = $