Moderate -0.3 This is a straightforward integration by parts question with a standard form (x^n·ln(x)). Students need to apply the integration by parts formula once, evaluate at limits, and simplify using logarithm laws. While it requires careful algebraic manipulation to reach the exact form requested, it follows a well-practiced technique with no conceptual surprises, making it slightly easier than average.
2 Find the exact value of \(\int _ { 1 } ^ { 3 } x ^ { 2 } \ln 3 x \mathrm {~d} x\). Give your answer in the form \(a \ln b + c\), where \(a\) and \(c\) are rational and \(b\) is an integer.
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2 Find the exact value of $\int _ { 1 } ^ { 3 } x ^ { 2 } \ln 3 x \mathrm {~d} x$. Give your answer in the form $a \ln b + c$, where $a$ and $c$ are rational and $b$ is an integer.\\
\includegraphics[max width=\textwidth, alt={}, center]{656df2a8-fc4d-49f3-a649-746103b4576e-04_2720_38_105_2010}
\hfill \mbox{\textit{CAIE P3 2024 Q2 [5]}}