Mathematics

# $\displaystyle \int_{e^{e^{e}}}^{e^{e^{e^{e}}}}\frac{dx}{xlnx\cdot ln\left ( lnx \right )\cdot ln\left ( ln\left ( lnx \right ) \right )}$ equals

1

##### SOLUTION
Let $\displaystyle I=\int _{ { e }_{ { e }_{ e } } }^{ { e }^{ { e }^{ { e }^{ e } } } }{ \frac { 1 }{ x\log { x } .\log { \left( \log { x } \right) . } \log { \left( \log { \left( \log { x } \right) } \right) } } } dx$

Substitute $\displaystyle \log { \left( \log { x } \right) } =t\Rightarrow \frac { 1 }{ x\log { x } } dx=dt$

$\displaystyle I=\int _{ e }^{ { { e }^{ e } } }{ \frac { 1 }{ t\log { t } } dt } =\left[ \log { \log { t } } \right] _{ e }^{ { e }^{ e } }=\left[ 1-0 \right] =1$

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Single Correct Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

#### Realted Questions

Q1 Single Correct Medium
If $y = \frac{1}{x}$, then value of $\int \ ydx$ is
• A. $log_{10}x+c$
• B. $log_e \Big \lgroup \frac{1}{x} \Big \rgroup + c$
• C. $log_{10} \Big \lgroup \frac{1}{x} \Big \rgroup + c$
• D. $log_ex + c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int_{\pi /5}^{3\pi /10}\frac{\cos x}{\cos x+\sin x}dx$is equal to
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• D. none of these

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
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Q4 Subjective Medium
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