Mathematics

# Evaluate:$\int { \left[ \sin { \left( \log { x } \right) } +\cos { \left( \log { x } \right) } \right] } dx$

##### SOLUTION
$I=\displaystyle \int \sin(\log x)+\cos(\log x)dx$
$\log x=t$
$x=e^{t}$
$dx=e^{t}dt$
$\therefore I=\displaystyle \int (\sin t+\cos t)e^{t}dt$
$=\displaystyle \int d(\sin te^{t})$
$=\sin te^{t}+c$
$=x \sin(\log x)+c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 128

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Q5 Passage Hard
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