Anastasiya-Romanova 秀

Yevpatoria, Republic of Crimea, Russia

http://www.quora.com/Anastasiya-Romanova

三十六计走为上计

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Compute $\int_0^{\pi/4}\frac{(1-x^2)\ln(1+x^2)+(1+x^2)-(1-x^2)\ln(1-x^2)}{(1-x^4)(1+x^2)} x\exp(\frac{x^2-1}{x^2+1}) dx$

calculus real-analysis integration definite-integrals closed-form asked May 31, 2014 at 10:25

math.stackexchange.com

58 votes

Evaluating $\int_0^\infty \frac{dx}{\sqrt{x}[x^2+(1+2\sqrt{2})x+1][1-x+x^2-x^3+...+x^{50}]}$

calculus integration definite-integrals improper-integrals closed-form asked Oct 17, 2014 at 17:50

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47 votes

Evaluating $\int_0^{\frac{\pi}{2}}\ln\left(\frac{\ln^2\sin\theta}{\pi^2+\ln^2\sin\theta}\right)\,\frac{\ln\cos\theta}{\tan\theta}\,d\theta$

calculus real-analysis integration definite-integrals contest-math asked Oct 22, 2014 at 11:25

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44 votes

How does math work in Anastasiya's world?

code-golf math repeated-transformation asked Aug 24, 2016 at 9:12

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42 votes

Prove $\int_{0}^{\pi/2} \ln \left(x^{2} + (\ln\cos x)^2 \right) \, dx=\pi\ln\ln2 $

calculus integration definite-integrals improper-integrals closed-form asked Aug 31, 2014 at 18:58

math.stackexchange.com

38 votes

A closed form of $\sum_{k=1}^\infty\frac{(-1)^{k+1}}{k!}\Gamma^2\left(\frac{k}{2}\right)$

calculus sequences-and-series summation factorial gamma-function asked Jul 26, 2014 at 4:22

math.stackexchange.com

37 votes

Closed form of $\mathscr{R}=\int_0^{\pi/2}\sin^2x\,\ln\big(\sin^2(\tan x)\big)\,\,dx$

calculus real-analysis integration closed-form asked Nov 4, 2014 at 17:14

math.stackexchange.com

35 votes

Looking for closed-forms of $\int_0^{\pi/4}\ln^2(\sin x)\,dx$ and $\int_0^{\pi/4}\ln^2(\cos x)\,dx$

real-analysis calculus integration improper-integrals harmonic-numbers asked Sep 2, 2014 at 15:45

math.stackexchange.com

35 votes

Closed-form of $\sum_{n=1}^\infty\frac{(-1)^{n+1}}{n}\Psi_3(n+1)=-\int_0^1\frac{\ln(1+x)\ln^3 x}{1-x}\,dx$

real-analysis calculus integration sequences-and-series harmonic-numbers asked Sep 17, 2014 at 12:43

math.stackexchange.com

34 votes

Integral of Combination Log and Inverse Trig Function

calculus integration definite-integrals improper-integrals closed-form asked Sep 11, 2014 at 10:21

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Top Answers

138

Find the value of $\sqrt{10\sqrt{10\sqrt{10...}}}$

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This isn't rocket science

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Really advanced techniques of integration (definite or indefinite)

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Surely You're Joking, Mr. Feynman! $\int_0^\infty\frac{\sin^2x}{x^2(1+x^2)}\,dx$

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Make 5 5 5 5 = 19

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How to prove $\int_{-\infty}^{+\infty} f(x)dx = \int_{-\infty}^{+\infty} f\left(x - \frac{1}{x}\right)dx?$

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Evaluating $\lim_{x\to 0}\left(\frac{1}{\sin x} - \frac{1}{\tan x}\right)$

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Prove that $\int_0^\pi\frac{\cos x \cos 4x}{(2-\cos x)^2}dx=\frac{\pi}{9} (2160 - 1247\sqrt{3})$

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Evaluating $\int \frac{\sec^2 x}{(\sec x + \tan x )^{{9}/{2}}}\,\mathrm dx$

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Prove that the infinite sum $\sum_{n=1}^{\infty} \frac{F_{n}}{ 10 ^ n }$ converges to a rational number

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Why does the hard-looking integral $\int_{0}^{\infty}\frac{x\sin^2(x)}{\cosh(x)+\cos(x)}dx=1$?

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Daunting series of integrals: $\sum_{n=2}^\infty\int_0^{\pi/2}\sqrt{\frac{(1-\sin x)^{n-2}}{(1+\sin x)^{n+2}}}\log(\frac{1-\sin x}{1+\sin x})dx$

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Evaluation of $\int_0^{\pi/4} \sqrt{\tan x} \sqrt{1-\tan x}\,\,dx$

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Calculation of $\int_{0}^{\frac{\pi}{4}}\tan^{-1}\sqrt{\frac{\cos 2x }{2 \cos^2 x}}dx$

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Highlight the Bounding Box, Part I: Cartesian Grid

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Creating a Crossed Square

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Visually deceptive "proofs" which are mathematically wrong

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Make 6 5 4 3 = 81

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Evaluate the indefinite integral:

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Evaluating by real methods $\int_0^{\pi/2} \frac{x^5}{2-\cos^2(x)}\ dx$

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what's the inverse of the quantile function on a pandas Series?

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Create a sequence between two letters

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Is Excel VBA's Rnd() really this bad?

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The entry-level PhD integral: $\int_0^\infty\frac{\sin 3x\sin 4x\sin5x\cos6x}{x\sin^2 x\cosh x}\ dx$

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

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A challenging logarithmic integral $\int_0^1 \frac{\log(1+x)\log(1-x)}{1+x}dx$

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Finding $\int_{0}^{\pi/2} \frac{\tan x}{1+m^2\tan^2{x}} \mathrm{d}x$

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Simplest way to integrate $\int \frac{1}{1+\tan x}dx,$

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Using differentiation under integral sign to calculate $\int^{\pi/2}_0\frac{\log(1+a\sin\phi)}{\sin\phi}d\phi$

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Fill formula down till last row in column

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