मान लीजिए f(x) = x, f_1(x) = f(log x), f_2(x) | vedclass

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(C) पैटर्न का अवलोकन करें: $f_1(x) = \log x$, $f_2(x) = \log(\log x)$, $f_3(x) = \log(\log(\log x))$।सामान्यतः, $f_n(x) = \underbrace{\log(\log(\dots\

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$f_{2027}(x) + c$

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(C) पैटर्न का अवलोकन करें: $f_1(x) = \log x$, $f_2(x) = \log(\log x)$, $f_3(x) = \log(\log(\log x))$।सामान्यतः, $f_n(x) = \underbrace{\log(\log(\dots\log x))}_{n 	ext{ बार}}$।मान लीजिए $I = \int \frac{1}{f(x) f_1(x) f_2(x) \dots f_{2026}(x)} dx$ है।ध्यान दें कि $\frac{d}{dx} f_{2027}(x) = \frac{d}{dx} (\log(f_{2026}(x))) = \frac{1}{f_{2026}(x)} \cdot \frac{d}{dx} f_{2026}(x)$।इस श्रृंखला नियम को जारी रखते हुए, $\frac{d}{dx} f_{2027}(x) = \frac{1}{f_{2026}(x) f_{2025}(x) \dots f_1(x) f(x)}$।अतः, $\int \frac{1}{f(x) f_1(x) \dots f_{2026}(x)} dx = f_{2027}(x) + c$।

मान लीजिए $f(x) = x$, $f_1(x) = f(\log x)$, $f_2(x) = f_1(\log x)$, $f_3(x) = f_2(\log x) \dots$ इत्यादि। तब $\int \frac{1}{f(x) f_1(x) f_2(x) \dots f_{2026}(x)} dx = \dots$

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