First slide

Methods of integration

Question

$\int \frac{\log (\log (\log x))}{x \log x \log (\log x)} d u = f (x) + C then f (x) =$

Moderate

A

$\frac{1}{2} (\log (\log x \log x))$
B

$\frac{1}{2} {(\log (\log x))}^{2}$
C

${(\log (\log (\log x)))}^{2}$
D

$\frac{1}{2} {(\log (\log (\log x)))}^{2}$

Solution

$I = \int \frac{\log (\log (\log x))}{x \log x \log (\log x)} d x$
$\begin{array}{l} Let \log (\log (\log x)) = t \\ I = \frac{1}{x \log x \log (\log x)} d x = d t \\ I = \int t d t = \frac{t^{2}}{2} + C \\ = \frac{(\log (\log (\log x)))^{2}}{2} + C \end{array}$

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