Mathematics

# Evaluate : $\displaystyle\int \left(\dfrac{1}{\log x} - \dfrac{1}{(\log x)^2} \right) . dx$

##### SOLUTION
$\displaystyle\int \left(\dfrac{1}{\log x} - \dfrac{1}{(\log x)^2} \right) . dx$
$=\displaystyle\int \left(\dfrac{1}{\log x} \right) . dx-$$\displaystyle\int \left( \dfrac{1}{(\log x)^2} \right) . dx = \left(\dfrac{x}{\log x} \right)+$$\displaystyle\int \left( \dfrac{1}{(\log x)^2} \right) . dx$$-\displaystyle\int \left( \dfrac{1}{(\log x)^2} \right) . dx$ [ Using method of by parts]
$= \left(\dfrac{x}{\log x} \right)+c$ [ Where $c$ is integrating constant]

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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