[tex] \int \frac{3 \: dx}{x.( \ln(3x)) {}^{2} } \: \to \: u = \ln(3x) \\ \\ \frac{du}{dx} = \frac{1}{3x} .3 \: \to \: \frac{du}{dx} = \frac{1}{x} \: \to \: du = \frac{dx}{x} \\ \\ \int \frac{3}{ (\ln(3x ))^{2} } . \frac{dx}{x} \: \to \: \int \frac{3 \: du}{u {}^{2} } \: \to \: 3 \int u {}^{ - 2} du \\ \\ 3 \int u {}^{ - 2} \: du = 3. \frac{u {}^{ - 2 + 1} }{ - 2 + 1} = 3. \frac{u {}^{ - 1} }{ - 1} = - 3. \frac{1}{u} = - 3. \frac{1}{ \ln(3x)} \\ \\ \boxed{- \frac{ 3}{ \ln(3x)} + c}[/tex]