HMMT 2016 T8

Compute

$\int_{0}^{\pi} \frac{2 \sin \theta+3 \cos \theta-3}{13 \cos \theta-5} \mathrm{~d} \theta .$

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

\frac{3 \pi}{13}-\frac{4}{13} \log \frac{3}{2}

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