Mathematics

# The integral  $\int \cos \left( \log _ { e } x \right) d x$  is equal to :(where  $C$  is a constant of integration)

$\dfrac { { x } }{ 2 } \left[ \cos \left( \log _{ { { e } } }{ x } \right) +\sin \left( \log _{ { { e } } }{ x } \right) \right] +{ C }$

##### SOLUTION
${ I }=\int \cos (\ell { n }{ x }){ d }{ x }$

${ I }=\cos (\ln { } { x })\cdot { x }+\int \sin (\ell { n }{ x }){ d }{ x }$

$\cos ( \ell n x ) x + \left[ \sin ( \ell n x ) \cdot x - \int \cos ( \ell n x ) d x \right]$

${ I }=\dfrac { { x } }{ 2 } [\sin (\ell { n }{ x })+\cos (\ell { n }{ x })]+{ C }$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

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Value of the integral $\displaystyle \int_{0}^{\pi}\frac{xdx}{1+\sin x}$, is
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• B. $\displaystyle \frac{\pi}{15}$
• C. $4\pi$
• D. $\pi$

1 Verified Answer | Published on 17th 09, 2020

Q2 One Word Medium
$\int { { e }^{ 3x } } \cdot { x }^{ 2 }dx$

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Q3 Single Correct Medium
$\int \dfrac {ln (\tan x)}{\sin x \cos x}dx$ is equal to
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1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Integrate:  $\dfrac{dy}{dx}=\left( { x }^{ 3 }+x+1 \right)$ w.r.t $x$

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