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• 57 Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $
• 45 Closed-form of $\int_0^1 \frac{\operatorname{Li}_2\left( x \right)}{\sqrt{1-x^2}} \,dx $
• 26 Ramanujan's approximation for $\pi$
• 24 Closed-form of $\int_0^1 \operatorname{Li}_3^3(x)\,dx$ and $\int_0^1 \operatorname{Li}_3^4(x)\,dx$
• 18 $\sum_{p \in \mathcal P} \frac1{p\ln p}$ converges or diverges?
• 17 Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $
• 17 Closed Form for the Imaginary Part of $\text{Li}_3\Big(\frac{1+i}2\Big)$
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