Question Number 222409 by Nicholas666 last updated on 25/Jun/25
$$ \\ $$$$\:\:\:\mathrm{Solve}\:;\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{ln}^{{n}} \:\mathrm{sin}\:\theta}{\mathrm{sin}^{{p}} \:\theta\:\mathrm{cos}^{{q}} \:\theta}\:\mathrm{d}\theta\:,\:\mathrm{for}\:{n},{p},{q}\:\in\:\mathbb{R}_{\geqslant\:\mathrm{0}} \:\:\:\:\:\:\:\: \\ $$$$ \\ $$