L'hopital rule, but how?

Calculus Level 3

C=limx(lnxx)\Large\mathfrak{\color{#D61F06}{C}}=\lim_{x\to\infty}\left(\dfrac{\ln x}{\lfloor x\rfloor}\right)

If you think that C\mathfrak{\color{#D61F06}{C}} does not exist or it is not finite submit 9.00, otherwise find: 05eCx dx\Large \displaystyle\int_0^5 e^{\mathfrak{\color{#D61F06}{C}}x}~\mathrm{d}x and submit your answer to two decimal places.

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