# 5 Short of 400 Followers

Calculus Level 4

\begin{align} \lambda&=\int_{0}^{1}\frac{dx}{1+x^{3}} \\ p&=\lim_{n\to \infty} \left[{\frac{\prod_{r=1}^{n}(n^{3}+r^{3})}{n^{3n}}}\right] ^{\frac{1}{n}}\end {align} If $$\lambda$$ and $$p$$ are given as above, find $$\ln(p)$$ in terms of $$\lambda$$.

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