First slide

Methods of integration

Question

$\int \frac{dx}{x (\log x) (\log \log x) \dots \underset{8 times}{\underset{⏟}{(\log \log \dots}} x)}$ is equal to

Moderate

A

$\underset{8 times}{\underset{⏟}{(\log \log \dots}} x) + C$
B

$\underset{7 times}{\underset{⏟}{(\log \log \dots}} x) + C$
C

$\underset{9 times}{\underset{⏟}{(\log \log \dots}} x) + C$
D

None of these

Solution

$\begin{array}{l} Let I = \int \frac{dx}{x (\log x) (\log \log x) \dots \underset{8 times}{\underset{⏟}{(\log \log \dots}} x)} \\ put, \underset{8 times}{\underset{⏟}{(\log \log \dots}} x) = t \end{array}$
$\begin{array}{l} \Rightarrow \frac{1}{\underset{7 times}{\underset{⏟}{(\log \log \dots}} x) \dots (\log \log x) (\log x) x} dx = dt \\ ∴ I = \int \frac{dt}{t} = \log t + C = \underset{9 times}{\underset{⏟}{(\log \log \log \dots}} x) + C \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App