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 69 What is $\int_0^1\frac{x^7-1}{\log(x)}\mathrm dx$? 68 Surprising identities / equations 40 A conjectured closed form of $\int\limits_0^\infty\frac{x-1}{\sqrt{2^x-1}\ \ln\left(2^x-1\right)}dx$ 27 How are the Taylor Series derived? 27 Prove that $x^3 + x^2 = 1$ has no rational solutions?

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 +20 Apéry's constant by triple integral -2 Find $\lim\limits_{{n \to \infty}} \frac1{2^n} \sum\limits_{k=1}^n \frac1{\sqrt{k}} \binom nk$ +10 How to obtain the identity $\sum_k\frac{(m-k)!}{(n-k)!} = \frac{(m+1-k)!}{(m+1-n)(n-k)!}$ +10 How many solutions are there to $x_{1} + x_{2} + x_{3} + x_{4} = 15$

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