Machinato

Member for 8 years, 7 months
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integration

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Answers

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Score Activity Newest

20

Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods?

Jun 5, 2016

18

Sum the series $\sum_{n = 1}^{\infty}\{\coth (n\pi x) + x^{2}\coth(n\pi/x)\}/n^{3}$

Jul 22, 2016

16

The Basel problem

Jun 8, 2017

13

Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$

Mar 2

10

The Basel problem

Jun 20, 2016

Questions

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34

Conjectured value of $\int_{0}^{\infty}\left(\frac{x-1}{\ln^2 x}-\frac{1}{\ln x}\right)\frac{\mathrm{d}x}{x^2+1}$

Jul 18, 2016

14

Closed form for $\sum_{n=1}^{\infty}\frac{1}{\sinh^2\!\pi n}$ conjectured

Jul 21, 2016

8

Closed form for $\sum_{n=1}^{\infty}\frac{(-1)^n}{\sqrt{n^2+a^2}}$

Jul 21, 2016

7

General formula for $\int^1_0 x^\alpha \log(1-x)\operatorname{Li}_2 (x)\, \mathrm dx$

Feb 7, 2021

6

Integrate $\int_{a}^1 \frac{\left(1-t^2\right) \tanh^{-1}t }{t^6} \ln \left(\frac{t+\sqrt{-1+t^2/a^2}}{t-\sqrt{-1+t^2/a^2}}\right) dt$

Nov 20, 2020

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integration

56

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25

posts

calculus

52

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22

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sequences-and-series

50

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15

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trigonometry

32

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5

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real-analysis

27

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5

posts

Reputation

+10

Closed form for $\sum_{n=1}^{\infty}\frac{1}{\sinh^2\!\pi n}$ conjectured

+40

Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$

+20

Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods?

+10

Mean distance between 2 points in a ball

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