Kemono Chen

A Chinese high school student, interested in evaluating integrals and other mathematical things.

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Evaluating $\int_0^1\ln(1+x^2)\ln(x^2+x^3)\frac{dx}{1+x^2}$

calculus integration definite-integrals asked Oct 13 '18 at 13:23

math.stackexchange.com

20 votes

Evaluate $\lim\limits_{x\to\infty}\frac1x\int_0^x\max\{\sin t,\sin(t\sqrt2)\}dt$

calculus integration definite-integrals asked Jul 22 '18 at 9:12

math.stackexchange.com

18 votes

Evaluating $\int_0^1\frac{x^{2/3}(1-x)^{-1/3}}{1-x+x^2}dx$

calculus integration definite-integrals hypergeometric-function asked Feb 24 at 11:37

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15 votes

Evaluate $\int_0^\infty{\frac{\tan x}{x^n}dx}$

calculus integration definite-integrals asked Mar 17 '18 at 22:33

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14 votes

Finding $\max |A|$ with $a_{ij}=\pm 1$

linear-algebra determinant asked Sep 10 '18 at 8:31

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13 votes

Evaluating $\int_0^{\pi/2}\operatorname{arcsinh}(2\tan x)dx$

calculus integration definite-integrals polylogarithm asked Jan 22 at 8:15

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13 votes

Entire function $f(z)$ grows like $\exp(x^\pi)$ as $x\to+\infty$

complex-analysis limits entire-functions asked Jan 15 at 5:52

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11 votes

Integral $\int_{\sqrt{33}}^\infty\frac{dx}{\sqrt{x^3-11x^2+11x+121}}$

integration definite-integrals elliptic-integrals asked Jan 18 at 13:41

math.stackexchange.com

11 votes

Convergence of $\sum_{n=1}^\infty\frac{\cot \varphi\pi n}{n^s}$

sequences-and-series number-theory convergence diophantine-approximation l-series asked Apr 13 at 6:03

math.stackexchange.com

11 votes

Evaluating $\int_0^\infty\frac{\ln(1+x^2)}{e^{\pi x}-1}dx$

calculus integration definite-integrals asked Sep 5 '18 at 9:08

math.stackexchange.com

Top Answers

Evaluate $\int_0^1 \log \left( \frac{x^2+\sqrt{3}x+1}{x^2-\sqrt{3}x+1} \right) \frac{dx}{x} $

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How to prove $\int_0^\infty \ln(1+\frac{z}{\cosh(x)})dx=\frac{\pi^2}{8}+\frac{(\cosh^{-1}(z))^2}{2},z\ge1$ and a closed form for $-1<z<1$?

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Solving $\int_{0}^{\infty} \frac{\sin(x)}{x^3}dx$

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Evaluating $\int_0^1\frac{\ln(1+x-x^2)}xdx$ without using poly logs.

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How to prove $\int_{-\infty}^{+\infty} \frac{x^2}{\cosh(x)^2} dx = \frac{\pi^2}{6}$?

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Compute polylog of order $3$ at $\frac{1}{2}$

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How to compute the limit,$\lim_{x\rightarrow 0}\frac{3x^2-3x\sin x}{x^2+x\cos1/x}$

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Is $\sqrt{x}$ an even function

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Kemono Chen

Evaluating $\int_0^1\ln(1+x^2)\ln(x^2+x^3)\frac{dx}{1+x^2}$

Evaluate $\lim\limits_{x\to\infty}\frac1x\int_0^x\max\{\sin t,\sin(t\sqrt2)\}dt$

Evaluating $\int_0^1\frac{x^{2/3}(1-x)^{-1/3}}{1-x+x^2}dx$

Evaluate $\int_0^\infty{\frac{\tan x}{x^n}dx}$

Finding $\max |A|$ with $a_{ij}=\pm 1$

Evaluating $\int_0^{\pi/2}\operatorname{arcsinh}(2\tan x)dx$

Entire function $f(z)$ grows like $\exp(x^\pi)$ as $x\to+\infty$

Integral $\int_{\sqrt{33}}^\infty\frac{dx}{\sqrt{x^3-11x^2+11x+121}}$

Convergence of $\sum_{n=1}^\infty\frac{\cot \varphi\pi n}{n^s}$

Evaluating $\int_0^\infty\frac{\ln(1+x^2)}{e^{\pi x}-1}dx$