$$\begin{align*} & \int_{0}^{\frac{\pi }{2}}{{{\ln }^{n}}\sin x\text{d}x} \\ & \int_{\frac{\pi }{4}}^{\frac{\pi }{2}}{\ln \left( \ln \tan x \right)}\text{d}x \\ \end{align*}$$
2026-05-14 10:07:19.1778753239
Two log trig integral
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The first integral is the log-sine integral. See this post to see how to evaluate it: Solve the integral $S_k = (-1)^k \int_0^1 (\log(\sin \pi x))^k dx$