Mathematics

# Evaluate the following integral$\int { \cfrac { 1 }{ x\log { x } } } dx$

##### SOLUTION
Let
$t=\log{x}\Rightarrow\,dt=\dfrac{1}{x}dx$

$\displaystyle\int{\dfrac{dx}{x\log{x}}}$

$=\displaystyle\int{\dfrac{dt}{t}}$

$=\log{\left|t\right|}+c$

$=\log{\left|\log{x}\right|}+c$ where $t=\log{x}$

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

#### Realted Questions

Q1 Single Correct Medium
Evaluate the integral
$\displaystyle \int^{\pi /4}_{0}\sec^{3}xdx$
• A. $\displaystyle \dfrac{1}{\sqrt{2}}-\dfrac{1}{2}\log(\sqrt{2}+1)$
• B. $2 \sqrt{2}\cdot \log{\sqrt{2}}$
• C. $\dfrac{1}{\sqrt{2}}l\mathrm{o}\mathrm{g}(\sqrt{2})$
• D. $\displaystyle \dfrac{1}{\sqrt{2}}+\dfrac{1}{2}\log(\sqrt{2}+1)$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\int {\cos e{c^m}x\cot x\,dx = }$
• A. $\frac{{{\rm{cose}}{{\rm{c}}^m}x}}{m} + C$
• B. $\frac{{ - 1}}{{m - 1}}{\rm{cose}}{{\rm{c}}^m}x + C$
• C. $\frac{1}{{m\,{{\sin }^m}x}} + C$
• D. $\frac{{ - 1}}{{m\,{{\sin }^m}x}} + C$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
$\displaystyle \int _{0}^{\pi}\dfrac{x}{a^{2}\cos^{2}{x}+b^{2}\sin^{2}{x}}\ dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int { \cfrac { x }{ 1+{ x }^{ 4 } } } dx$ is equal to
• A. $\cfrac { 1 }{ 2 } \cot ^{ -1 }{ { x }^{ 2 } } +C$
• B. $\cot ^{ -1 }{ { x }^{ 2 } } +C$
• C. $\tan ^{ -1 }{ { x }^{ 2 } } +C\quad$
• D. $\cfrac { 1 }{ 2 } \tan ^{ -1 }{ { x }^{ 2 } } +C\quad$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Subjective Medium
Find: $\int { { x }^{ 2 }.\log { x } dx }$.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020