Top network posts

• 53 Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $
• 43 Closed-form of $\int_0^1 \frac{\operatorname{Li}_2\left( x \right)}{\sqrt{1-x^2}} \,dx $
• 24 Ramanujan's approximation for $\pi$
• 23 Closed-form of $\int_0^1 \operatorname{Li}_3^3(x)\,dx$ and $\int_0^1 \operatorname{Li}_3^4(x)\,dx$
• 17 Under what conditions will the rectangle of the Japanese theorem be a square?
• 17 Fibonacci numbers and the nontrivial zeros of the Riemann zeta function
• 16 Prove that $\int_0^1 \frac{1}{1+\ln^2 x}\,dx = \int_1^\infty \frac{\sin(x-1)}{x}\,dx $
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