Question Bank [2022] — Maths STD 12 Science — Question
Maharashtra BoardEnglish MediumSTD 12 ScienceMathsQuestion Bank [2022]2 Marks
Question
$\int \frac{\log (\log x)}{x} d x$
✓
Answer
$\text { Let } I =\int \frac{\log (\log x)}{x} d x$
Put $\log x=t$
$ \therefore \frac{1}{x} d x= dt$
$\therefore I =\int \log t d t =\int \log t \cdot 1 dt$
$=\log t \int 1 \cdot dt -\int\left[\frac{ d }{ dt }(\log t ) \int 1 \cdot dt \right] dt$
$=\log t \cdot t -\int\left(\frac{1}{ t } \times t \right) dt$
$= t \cdot \log t -\int dt$
$= t \log t - t + c$
$= t (\log t -1)+ c$
$\therefore I =\log x [\log (\log x )-1]+ c $
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