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
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