Mathematics

# Integrate $\displaystyle \int \dfrac {\log x}{x^{2}}dx$

##### SOLUTION
$I=\displaystyle\int \underset{(I)}{log x}\underset{(II)}{\dfrac{1}{x^2}}dx$
By integration by parts,
$I=log x\left(\dfrac{-1}{x}\right)-\displaystyle\int \dfrac{1}{x}\cdot \left(\dfrac{-1}{x}\right)dx=\dfrac{-1}{x}log x+\displaystyle\int \dfrac{1}{x^2}dx$.
$I=\dfrac{-1}{x}log x\dfrac{-1}{x}+C$.

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

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