(4) \( (18\%) \) Calculate the following integrals and limits:

(a) $\int0^1 \frac{\ln(1+x)}{\ln(1+x)+\ln(2-x)} \, dx$ (b) $\lim{n\to\infty} \sqrt[n]{2^n + 3^n + 5^n + 7^n}$ (c) $\lim_{n\to\infty} \frac{\sqrt[n]{n!}}{n}$.