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Mathematics
Yuri Negometyanov's user avatar
Yuri Negometyanov's user avatar
Yuri Negometyanov's user avatar
Yuri Negometyanov
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24
Nested root integral $\int_0^1 \frac{dx}{\sqrt{x+\sqrt{x+\sqrt{x}}}}$
Aug 2, 2019
18
$x,y,z \geqslant 0$, $x+y^2+z^3=1$, prove $x^2y+y^2z+z^2x < \frac12$
May 27, 2016
16
How to find $\operatorname{P.V.}\int_0^1 \frac{1}{x (1-x)}\arctan \left(\frac{8 x^2-4 x^3+14 x-8}{2 x^4-3 x^3-11 x^2+16 x+16}\right) \textrm{d}x$?
Feb 7, 2021
13
Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$
Apr 25, 2023
12
How can we show that $\int_{-\infty}^{+\infty}{ke^x\pm1\over \pi^2+(e^x-x+1)^2}\cdot{(e^x+1)^2\over \pi^2+(e^x+x+1)^2}\cdot 2x \,\mathrm dx=k?$
May 12, 2017
12
Prove that $\int_0^\infty\frac1{x^x}\, dx<2$
Dec 26, 2020
12
Prove $7^{71}>75^{32}$
Mar 20, 2021
12
Prove $\left(\frac{a+1}{a+b}\right)^a+\left(\frac{b+1}{b+c}\right)^b+\left(\frac{c+1}{c+a}\right)^c \geqslant 3$
Aug 31, 2016
12
Is there an exact solution for $\large\int \frac{dx}{\tan^{-1}(x)}$?
Jul 22, 2021
11
How to evaluate $\sum_{k=3}^{\infty} \frac{\ln (k)}{k^2 - 4}$?
May 7, 2021
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МНК алгоритм
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Эффективнейшие методы для нахождения единиц в двоичном виде числа
10
Как убрать ошибки измерений?
9
Квадратный корень из числа
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Поиск числа, имеющего наибольшее число делителей