User TheSimpliFire

5 votes

Compare $2^{2016}$ and $10^{605}$ without a calculator

answered Jan 24, 2018 at 7:55

5 votes

Accepted

Evaluate indefinite integral $\int \tan(\frac{x}{3}) \, dx$

answered Jun 1, 2018 at 15:10

5 votes

What does the equal sign mean in mathematics?

answered Jun 4, 2018 at 9:54

5 votes

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Is $\sqrt[0]{0}$ defined?

answered Jul 15, 2018 at 10:41

5 votes

Composition of functions and number of solutions

answered Sep 7, 2018 at 17:41

5 votes

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Sum of roots of equation $x^4 - 2x^2 \sin^2(\displaystyle {\pi x}/2) +1 =0$ is

answered Aug 26, 2018 at 14:11

5 votes

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Differentiate $\tan^3(x^2)$

answered Aug 26, 2018 at 18:35

5 votes

A problem related with limit and continuity.

answered Aug 7, 2018 at 14:44

5 votes

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The closest value to $\int_0^1 \sqrt{1+\frac{1}{3x}} dx$?

answered Jan 15, 2019 at 13:29

5 votes

Prove: $\frac{1}{12} + \frac{1}{23} + \frac{1}{3*4} +⋯+ \frac{1}{n(n+1)}= \frac{n}{(n+1)}$

answered Mar 6, 2019 at 7:27

5 votes

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Compute the integral $I=\int_\gamma f(z)\, dz$, where $f(z)=\frac{e^{z^2}}{z^2-6z}$ and $\gamma=\{z:|z-2|=3\}$.

answered Mar 10, 2019 at 15:25

5 votes

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What is the maximum value of $\ln(x+\ln(x+\ln(x+\cdots)))-\ln x$?

answered Nov 9, 2018 at 16:06

5 votes

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Values of $x$ satisfying $\sin x\cdot\cos^3 x>\sin^3x\cdot\cos x$

answered Dec 1, 2018 at 19:00

5 votes

Big list: Free textbooks and resources

answered May 10, 2019 at 19:22

5 votes

Example of continuous periodic function with divergent Fourier series

answered Apr 27, 2019 at 7:44

5 votes

Accepted

Inscribed circle in a right-angled triangle

answered Apr 21, 2019 at 13:32

5 votes

Exact expression of a trigonometric integral

answered Mar 22, 2020 at 11:38

5 votes

Show the $\arcsin$ identity: $ \arcsin(1 - 2x) + 2\arcsin(\sqrt{x}) = \pi / 2$

answered Jun 23, 2020 at 20:28

5 votes

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Is the converse of Ramanujan's Master Theorem also true?

answered Aug 20, 2020 at 7:41

5 votes

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Show that $\int_0^\pi\int_0^\pi\frac{\sin(x) \sin(px) \cos(qy)}{\sin(x)^2 + \sin(y)^2}\,dx\,dy$ tends to $0$ as $p\to\infty$ or $q\to\infty$

answered Oct 24, 2020 at 14:36

5 votes

Prove that there are no composite integers $n=am+1$ such that $m \ | \ \phi(n)$

answered Oct 3, 2020 at 10:33

5 votes

Integral $\int_1^\infty\operatorname{arccot}\left(1+\frac{2\pi}{\operatorname{arcoth}x-\operatorname{arccsc}x}\right)\frac{\mathrm dx}{\sqrt{x^2-1}}$

answered Oct 4, 2021 at 16:22

5 votes

Compute the limit $\lim\limits_{t \to + \infty} \int_0^{+ \infty} \frac{ \mathrm d x}{e^x+ \sin tx} $

answered Nov 2, 2020 at 9:04

5 votes

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Find maximum and minimum of $\sin x + \sin y$

answered Jun 15, 2019 at 13:55

4 votes

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Show $\lim\limits_{t\to\infty}\Bigg|\sum\limits_{n=0}^\infty\Theta(t-nR)\frac{(\Gamma(t-nR))^n}{n!}e^{-\Gamma(t-nR)}\Bigg|^2=\frac1{(1+\Gamma R)^2}$

answered Jul 29, 2021 at 15:33

4 votes

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Solving the integral $\int_{0}^{1} d{v} \frac{e^{-y^2(1+v^2)}}{1+v^2}e^{\frac{2 t v^2}{v^2+1}}$

answered Aug 31, 2021 at 8:29

4 votes

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Prove $\sqrt{2} \notin \mathbb{Q}(\sqrt{3+\sqrt{3}})$ using field trace

answered Nov 12, 2021 at 11:49

4 votes

Maximizing the ratio $\|p\|_\infty/\|p\|_2^2$ for a probability distribution $p$ on $n$ elements

answered Apr 10, 2021 at 9:07

4 votes

Accepted

Show that $\frac{\arctan(x^2)}{\ln(1+x^2)}$ is bounded by $\frac{1+\sqrt{2}}{2}$

answered Mar 21, 2021 at 9:45

4 votes

Finding the value of $\alpha^2\beta+\beta^2\gamma+\gamma^2\alpha$

answered Mar 28, 2021 at 9:47

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808 Answers

Compare $2^{2016}$ and $10^{605}$ without a calculator

Evaluate indefinite integral $\int \tan(\frac{x}{3}) \, dx$

What does the equal sign mean in mathematics?

Is $\sqrt[0]{0}$ defined?

Composition of functions and number of solutions

Sum of roots of equation $x^4 - 2x^2 \sin^2(\displaystyle {\pi x}/2) +1 =0$ is

Differentiate $\tan^3(x^2)$

A problem related with limit and continuity.

The closest value to $\int_0^1 \sqrt{1+\frac{1}{3x}} dx$?

Prove: $\frac{1}{12} + \frac{1}{23} + \frac{1}{3*4} +⋯+ \frac{1}{n(n+1)}= \frac{n}{(n+1)}$

Compute the integral $I=\int_\gamma f(z)\, dz$, where $f(z)=\frac{e^{z^2}}{z^2-6z}$ and $\gamma=\{z:|z-2|=3\}$.

What is the maximum value of $\ln(x+\ln(x+\ln(x+\cdots)))-\ln x$?

Values of $x$ satisfying $\sin x\cdot\cos^3 x>\sin^3x\cdot\cos x$

Big list: Free textbooks and resources

Example of continuous periodic function with divergent Fourier series

Inscribed circle in a right-angled triangle

Exact expression of a trigonometric integral

Show the $\arcsin$ identity: $ \arcsin(1 - 2x) + 2\arcsin(\sqrt{x}) = \pi / 2$

Is the converse of Ramanujan's Master Theorem also true?

Show that $\int_0^\pi\int_0^\pi\frac{\sin(x) \sin(px) \cos(qy)}{\sin(x)^2 + \sin(y)^2}\,dx\,dy$ tends to $0$ as $p\to\infty$ or $q\to\infty$

Prove that there are no composite integers $n=am+1$ such that $m \ | \ \phi(n)$

Integral $\int_1^\infty\operatorname{arccot}\left(1+\frac{2\pi}{\operatorname{arcoth}x-\operatorname{arccsc}x}\right)\frac{\mathrm dx}{\sqrt{x^2-1}}$

Compute the limit $\lim\limits_{t \to + \infty} \int_0^{+ \infty} \frac{ \mathrm d x}{e^x+ \sin tx} $

Find maximum and minimum of $\sin x + \sin y$

Show $\lim\limits_{t\to\infty}\Bigg|\sum\limits_{n=0}^\infty\Theta(t-nR)\frac{(\Gamma(t-nR))^n}{n!}e^{-\Gamma(t-nR)}\Bigg|^2=\frac1{(1+\Gamma R)^2}$

Solving the integral $\int_{0}^{1} d{v} \frac{e^{-y^2(1+v^2)}}{1+v^2}e^{\frac{2 t v^2}{v^2+1}}$

Prove $\sqrt{2} \notin \mathbb{Q}(\sqrt{3+\sqrt{3}})$ using field trace

Maximizing the ratio $\|p\|_\infty/\|p\|_2^2$ for a probability distribution $p$ on $n$ elements

Show that $\frac{\arctan(x^2)}{\ln(1+x^2)}$ is bounded by $\frac{1+\sqrt{2}}{2}$

Finding the value of $\alpha^2\beta+\beta^2\gamma+\gamma^2\alpha$