Let f(x) = x, f_1(x) = f(log x), f_2(x) = f_1 | vedclass

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(C) Observe the pattern: $f_1(x) = \log x$, $f_2(x) = \log(\log x)$, $f_3(x) = \log(\log(\log x))$.In general, $f_n(x) = \underbrace{\log(\log(\dots\l

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$f_{2027}(x) + c$

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(C) Observe the pattern: $f_1(x) = \log x$, $f_2(x) = \log(\log x)$, $f_3(x) = \log(\log(\log x))$.In general, $f_n(x) = \underbrace{\log(\log(\dots\log x))}_{n 	ext{ times}}$.Let $I = \int \frac{1}{f(x) f_1(x) f_2(x) \dots f_{2026}(x)} dx$.Note that $\frac{d}{dx} f_{2027}(x) = \frac{d}{dx} (\log(f_{2026}(x))) = \frac{1}{f_{2026}(x)} \cdot \frac{d}{dx} f_{2026}(x)$.Continuing this chain rule, $\frac{d}{dx} f_{2027}(x) = \frac{1}{f_{2026}(x) f_{2025}(x) \dots f_1(x) f(x)}$.Thus, $\int \frac{1}{f(x) f_1(x) \dots f_{2026}(x)} dx = f_{2027}(x) + c$.

Let $f(x) = x$, $f_1(x) = f(\log x)$, $f_2(x) = f_1(\log x)$, $f_3(x) = f_2(\log x) \dots$ and so on. Then $\int \frac{1}{f(x) f_1(x) f_2(x) \dots f_{2026}(x)} dx = \dots$

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