Mathematics
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whitexlotus
  • Member for 6 years, 11 months
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12 Questions

Score Activity Newest Views
16 votes
3 answers
1k views

Rare Integral $\int_0^1 \frac{\cosh \left( \alpha \cos ^{-1}x \right)\cos \left( \alpha \sinh ^{-1}x \right)}{\sqrt{1-x^{2}}} dx$

11 votes
2 answers
271 views

Find the lowest value of $n$, such that the equation $p^{2}+pq+q^{2}=n$ has only five solutions

8 votes
1 answer
275 views

Alternative proof that $\frac{\sqrt[3]3}{\sqrt[2]2}\cdot\frac{\sqrt[5]5}{\sqrt[4]4}\cdot\frac{\sqrt[7]7}{\sqrt[6]6}\cdot ...=2^{-\gamma+\log\sqrt2}$

4 votes
0 answers
133 views

Rare sum with Trigamma function $\left( -1 \right)^{n-1}\left( \psi _{1}\left( n \right) \right)^{2}$

3 votes
1 answer
106 views

Dilogarithm integral $\int_0^{\infty} \frac{x^{s/2-1}}{1+x^s} \text{Li}_2(-x) dx=- \frac{\pi^3}{4} \left( \frac1{3 s}+ \frac1{ s^3}\right)$

3 votes
1 answer
108 views

Hard Integral $\int\limits_0^1 \frac{\ln y\operatorname{Li}_2 (-y)}{1-y^2} \, dy$

3 votes
1 answer
105 views

Inequality $\frac{x_1^2}{x_1^2+x_2x_3}+\frac{x_2^2}{x_2^2+x_3x_4}+\cdots+\frac{x_{n-1}^2}{x_{n-1}^2+x_nx_1}+\frac{x_n^2}{x_n^2+x_1x_2}\le n-1$

3 votes
2 answers
186 views

Inequality $\frac{1}{a+b}+\frac{1}{a+2b}+...+\frac{1}{a+nb}<\frac{n}{\sqrt{a\left( a+nb \right)}}$

2 votes
1 answer
115 views

Hard inequality with cos() and sin()

2 votes
1 answer
177 views

Hard Integral $\int\limits_{-1}^{1}{\frac{\arctan x}{1+x}\ln \frac{1+x^{2}}{2}dx}=\frac{\pi ^{3}}{96}$ [duplicate]

2 votes
2 answers
757 views

Calculate the closed form of $\frac{\sqrt[5]{5}}{\sqrt[3]{3}}\cdot \frac{\sqrt[9]{9}}{\sqrt[7]{7}}\cdot \frac{\sqrt[13]{13}}{\sqrt[11]{11}}\cdot ...$

1 vote
0 answers
84 views

Hard system, Three equations, three variables