Mathematics

# $\int { \log { \left( \log { x } \right) +\dfrac { 1 }{ \log { x } } } } dx$

$x\log { \left( \log { x } \right) +c }$

##### SOLUTION
$\int {\left[ {\log x\left( {\log x} \right) + \dfrac{1}{{\log x}}} \right]} dx$
$= \int {1.\log \left( {\log x} \right)dx + \int {\dfrac{1}{{\log x}}} }$
$= \log \left( {\log x} \right).x-\int {\dfrac{1}{{\log x}} \times \dfrac{1}{x} \times xdx + \int {\dfrac{{dx}}{{\log x}}} }$
$= x\log \left( {\log x} \right) - \int {\dfrac{{dx}}{{\log x}} + \int {\dfrac{{dx}}{{\log x}}} }$
$= x\log \left( {\log x} \right) + c$

Its FREE, you're just one step away

Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 109

#### Realted Questions

Q1 Subjective Medium
Evaluate the following integrals:$\displaystyle \int {\dfrac{2x-7}{\sqrt{4x-1}}.dx}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If $f(x) = \dfrac {x + 2}{2x + 3}$, then $\displaystyle \int \left (\dfrac {f(x)}{x^{2}}\right )^{1/2} dx = \dfrac {1}{\sqrt {2}}g \left (\dfrac {1 + \sqrt {2f(x)}}{1 - \sqrt {2f(x)}}\right ) - \sqrt {\dfrac {2}{3}}h \left (\dfrac {\sqrt {3f(x)} + \sqrt {2}}{\sqrt {3f(x)} - \sqrt {2}}\right ) + c$, where
• A. $g(x) = \log |x|, h(x) = \tan^{-1}x$
• B. $g(x) = h(x) = \tan^{-1}x$
• C. $g(x) = \log|x|, h(x) = \log |x|$
• D. $g(x) = \tan^{-1} x, h(x) = \log |x|$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\displaystyle \int\frac{dx}{1-\sin^{4}x}=$
• A. $\displaystyle \frac{1}{2} \left[\tan x-\frac{1}{\sqrt{2}}\tan^{-1}(\sqrt{2} \tan x) \right] +c$
• B. $\displaystyle \frac{1}{2} \left[\tan x+\frac{1}{2\sqrt{2}} \cot^{-1}(\sqrt{2} \tan x) \right ] +c$
• C. $\displaystyle \frac{1}{2} \left[ \tan x-\frac{1}{2\sqrt{2}}\cot^{-1}(\sqrt{2} \tan x) \right ] +c$
• D. $\displaystyle \frac{1}{2} \left[\tan x+\frac{1}{\sqrt{2}} \tan^{-1} (\sqrt{2} \tan x) \right] +c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
$\int \frac{x^{2}+x-6}{(x-2)(x-1)}dx=$

Evaluate $\int \dfrac{e^x-e^{-x}}{e^x+e^{-x}}dx$