Product Integral

Calculus Level 4

Rather than the traditional integral, we define the product integral as

\[\circ_a^bf(x)^{dx}=\lim_{n\to\infty}\prod_{i=1}^nf(x_i)^{\Delta x_i}\]

If

\[N=\circ_0^{100}(2x+5)^{dx}\]

then what is the value of \(\left\lfloor \log_e N\right\rfloor\)?

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