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Need solution for RD Sharma maths class 12 chapter 19 Definite Integrals exercise Very short answer type question 28

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Answer: \log _{e} 2

Hint: you must know the rule of integration

Given: \int_{e}^{e^{2}} \frac{1}{x \log x} d x

Solution:  Put \log x=t

\frac{d x}{x}=\mathrm{dt}

\begin{aligned} &=\int_{e}^{e^{2}} \frac{1}{t} d t \\\\ &=[\log \mid t]_{-e}^{e^{2}} \end{aligned}

\begin{aligned} &=[\log [\log x]]_{e}^{e^{2}} \\\\ &=\log \left(\log e^{2}\right)-\log (\log e) \\\\ &=\log (2 \log e)-\log (1) \\\\ &=\log 2 \end{aligned}

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