# 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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