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∫ 1 X Log X D X - Mathematics

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प्रश्न

\[\int\frac{1}{x \log x} dx\]
योग
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उत्तर

\[\text{Here, we are considering }\text{log x  as} \log_e x . \]
\[\text{Let I} = \int\frac{1}{x \log x}dx\]
\[\text{Putting }\log x = t\]
\[ \Rightarrow \frac{1}{x} = \frac{dt}{dx}\]
\[ \Rightarrow \frac{1}{x}dx = dt\]
\[ \therefore I = \int\frac{1}{t}dt\]
\[ = \text{log} \left|  \text{log x} \right| + C\]

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अध्याय 19: Indefinite Integrals - Exercise 19.08 [पृष्ठ ४७]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 19 Indefinite Integrals
Exercise 19.08 | Q 18 | पृष्ठ ४७

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