Solving ln in Integration - Any Hints? (Coffee)

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SUMMARY

The discussion focuses on solving the integral $\displaystyle \int\frac{ln^2\,3x}{x}dx$. Participants recommend using the substitution \(u=\ln(3x)\) to simplify the integration process. Additionally, it is emphasized that when encountering a natural logarithm in the numerator and a variable in the denominator, a substitution involving \(u = \ln(x)\) is often effective. This approach streamlines the integration and leads to a more manageable expression.

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can someone give me hints how to solve this.(Coffee)

$\displaystyle \int\frac{ln^2\,3x}{x}dx$
 
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paulmdrdo said:
can someone give me hints how to solve this.(Coffee)

$\displaystyle \int\frac{ln^2\,3x}{x}dx$

Hi paulmdrdo, :)

Substitute \(u=\ln(3x)\).
 
paulmdrdo said:
can someone give me hints how to solve this.(Coffee)

$\displaystyle \int\frac{ln^2\,3x}{x}dx$
To add to Sudharaka's sage suggestion, whenever you have a ln in numerator and x in the denominator of the integrand, some kind of u = ln(x) substitution bears looking into.

-Dan
 

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