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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals2 Marks
Question
Integrate the function: $\frac{{{{\left( {\log x} \right)}^2}}}{x}$
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Answer

Putting log x = t
$ \Rightarrow \frac{dx}{x} = {{dt}}{{}}$
$\therefore \int {\frac{{{{\left( {\log x} \right)}^2}}}{x}dx} $ $ = \int {{t^2}dt} $
$= \frac{{{t^3}}}{3} + c$
$= \frac{1}{3}{\left( {\log x} \right)^3} + c$

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