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• 91 Conjecture $\int_0^1\frac{\mathrm dx}{\sqrt{1-x}\ \sqrt[4]x\ \sqrt[4]{2-x\,\sqrt3}}\stackrel?=\frac{2\,\sqrt2}{3\,\sqrt[8]3}\pi$
• 67 Is $0.1010010001000010000010000001 \ldots$ transcendental?
• 62 Integral $\int_0^1\frac{\ln\left(x+\sqrt2\right)}{\sqrt{2-x}\,\sqrt{1-x}\,\sqrt{\vphantom{1}x}}\mathrm dx$
• 60 What are some examples of mathematics that had unintended useful applications much later?
• 54 Find $xy+yz+zx$ given systems of three homogenous quadratic equations for $x, y, z$
• 51 Conjecture $\int_0^1\frac{dx}{\sqrt[3]x\,\sqrt[6]{1-x}\,\sqrt{1-x\left(\sqrt{6}\sqrt{12+7\sqrt3}-3\sqrt3-6\right)^2}}=\frac\pi9(3+\sqrt2\sqrt[4]{27})$
• 50 Why does Wolframalpha think that this sum converges?
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