# Anastasiya-Romanova 秀

less info
reputation
32282
bio website quora.com/Anastasiya-Romanova location Yevpatoria, Republic of Crimea, Russia age 14 member for 9 months seen Dec 14 at 15:32 profile views 7,434

Romanov's dream : $$\color{red}{\int_0^1 x^2 x^{\Large x^2}\ln^2x\;dx=}\small\frac{1\cdot2}{(1+2)^3}-\frac{2\cdot3}{(2+3)^4}+\frac{3\cdot4}{(3+4)^5}-\frac{4\cdot5}{(4+5)^6}+\cdots$$

If you're interested in having conversation with me, feel free to contact me at Quora. I will reply every substantial message that comes to me if I'm not busy with my school or course stuffs.

Here are other sites where I participate: (if you find other than these four, I can assure you it does not belong to me)

Anyway, please do visit The Monster Integral and Integral Contest. Thank you... ❤(ˆ‿ˆԅ)

 69 Find the value of $\sqrt{10\sqrt{10\sqrt{10…}}}$ 26 Surely You're Joking, Mr. Feynman! $\int_0^\infty\frac{\sin^2x}{x^2(1+x^2)}\,dx$ 20 Evaluating $\displaystyle\lim_{x\to 0}\left(\frac{1}{\sin x} - \frac{1}{\tan x}\right)$ 19 Prove that $\int_0^\pi\frac{\cos x \cos 4x}{(2-\cos x)^2}dx=\frac{\pi}{9} (2160 - 1247\sqrt{3})$ 15 Evaluate the indefinite integral $\int \frac{\sqrt{9-4x^{2}}}{x}dx$

# 7,986 Reputation

 +10 The Monster Integral +20 Evaluating $\displaystyle\lim_{x\to 0}\left(\frac{1}{\sin x} - \frac{1}{\tan x}\right)$ +5 An exercise from my brother: $\int_{-1}^1\frac{\ln (2x-1)}{\sqrt[\large 6]{x(1-x)(1-2x)^4}}\,dx$ +5 Prove $\int_{0}^{\pi/2} x\csc^2(x)\arctan \left(\alpha \tan x\right)\, dx = \frac{\pi}{2}\left[\ln\frac{(1+\alpha)^{1+\alpha}}{\alpha^\alpha}\right]$

# 41 Questions

 45 The Monster Integral 36 The Wicked Integral 28 Integral Contest 27 Closed form of $\displaystyle\mathscr{R}=\int_0^{\frac{\pi}{2}}\sin^2x\,\ln\big(\sin^2(\tan x)\big)\,\,dx$ 27 Prove $\displaystyle \int_{0}^{\pi/2} \ln \left(x^{2} + (\ln\cos x)^2 \right) \, dx=\pi\ln\ln2$

# 76 Tags

 359 calculus × 113 104 limits × 8 332 integration × 100 99 trigonometry × 26 248 definite-integrals × 73 81 algebra-precalculus × 10 139 real-analysis × 47 80 radicals × 3 112 improper-integrals × 38 74 closed-form × 27

# 3 Accounts

 Mathematics 7,986 rep 32282 Anime & Manga 146 rep 16 Stack Overflow 101 rep 4