Question

` ∫  log x / x  dx `

 

 

 

Answer 1

\[\int\frac{\log x}{x}dx\]

\[Let, \log x = t\]

\[ \Rightarrow \frac{1}{x} = \frac{dt}{dx}\]

\[Now, \int\frac{\log x}{x}dx\]

 = ∫ t . dt

\[ = \frac{t^2}{2} + C\]

\[ = \frac{\left( \log x \right)^2}{2} + C\]