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
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