Optimization, Mathematics.
is small, hence we can approximate $1–1/i$ as $\text{exp}(-1/i)$, obtained from series expansion of $\text{exp}(-x)$ $$\text{exp}(-x)=1-x + O(x²) $$ Use this approximation to simplify the integral in Eq $\ref{defInt}$ $$L(s)\approx \int_{1}^n \frac{\text{exp}(-2s/i)}{i} \mathrm{d}i\approx