Mathematics

# Evaluate :$\displaystyle \int { \log } x{dx}$

##### SOLUTION
Let $I=\displaystyle\int \log x dx$

Let $y=\log x$

$\therefore x=e^y$

$\therefore$ using integration by parts

$I=\displaystyle\int y dx=xy-\displaystyle\int x dy$

$=x log x-\displaystyle\int e^ydy$

$=x log x -e^y$

$=x log x-e^{log x}+x$                $[\because e^{log^x_e}=x]$

$I=xlog x-x+c$.

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

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