MHB Solving ln in Integration - Any Hints? (Coffee)

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To solve the integral ∫(ln²(3x)/x)dx, a common approach is to use the substitution u = ln(3x). This substitution simplifies the integral by transforming the logarithmic expression. Additionally, when encountering a logarithm in the numerator and x in the denominator, considering a u = ln(x) substitution can be beneficial. This method is often effective for integrals involving logarithmic functions. Utilizing these substitution techniques can lead to a clearer path to the solution.
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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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