Mathematics

# Evaluate the following integral:$\int { \cfrac { \sin { \left( \log { x } \right) } }{ x } } dx\quad$

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

$\displaystyle\int{\dfrac{\sin{\left(\log{x}\right)}}{x}dx}$

$=\displaystyle\int{\sin{t}\,dt}$

$=-\cos{t}+c$

$=-\cos{\left(\log{x}\right)}+c$ where $t=\log{x}$

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

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