Mathematics

# Simplify:-$\int {\left( {\dfrac{1}{{\left( {\ln x} \right)}} - \dfrac{1}{{{{\left( {\ln x} \right)}^2}}}} \right)} dx$

##### SOLUTION
$\displaystyle\int \left(\dfrac{1}{\ln x}-\dfrac{1}{(\ln x)^{2}}\right)\ dx$
Put $\ln x=t,\dfrac{dx}{x}=dt$
$dx=x\ dt$
$dx=e^{t}dt$
$\displaystyle\int e^{t}\left(\dfrac{1}{t}-\dfrac{1}{t^{2}}\right) dt$
We know that $\displaystyle\int e^{x}(f(x)+f(x))dx=e^{x}f(x)+c$
$=\dfrac{e^{t}}{t}+c$
$=\dfrac{x}{\ln x}+c=\dfrac{x}{\ln x}+c$

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

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