User Kamal Saleh - Mathematics Stack Exchange

14 votes

7 answers

960 views

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

asked Feb 17 at 18:22

8 votes

7 answers

2k views

Approximating cube roots to high precision.

asked Jul 17, 2023 at 21:45

7 votes

3 answers

292 views

Solve $\int_0^\infty\frac x{e^x-e^{\frac x2}}dx$

asked Jul 24, 2023 at 1:28

7 votes

3 answers

301 views

Proving that $\lim_{x\rightarrow0}\frac{H_x}x=\frac{\pi^2}6$

asked Mar 9, 2023 at 4:29

6 votes

3 answers

167 views

Find $f(x)$ such that $\sum_{k=0}^{\infty}f^k\left(x\right)=\sum_{k=0}^{\infty}f^{\left(k\right)}\left(x\right)$

asked Aug 30, 2023 at 17:46

6 votes

0 answers

204 views

Is $\sum_{k=1}^\infty \frac{1}{p_{p_k}}$, where $p_k$ is the $k$-th prime, irrational? transcendental?

asked Nov 12, 2022 at 21:31

6 votes

3 answers

528 views

Proof of $\int_0^1\ln\left(\frac{1}{\ln \frac{1}{x}}\right)dx=\gamma$

asked Jan 2, 2023 at 17:43

6 votes

2 answers

331 views

Calculate $\int_{-\infty}^\infty\frac{x^2}{1+x^8}dx$

asked Feb 1, 2023 at 16:01

6 votes

2 answers

368 views

Imaginary numbers and partial fraction decomposition in integration

asked Feb 9, 2023 at 19:02

6 votes

1 answer

280 views

How to find $\int_0^\infty\frac{x!}{x^x}dx$

asked Feb 14, 2023 at 17:05

6 votes

1 answer

788 views

2023 MIT Integration Bee Regular Season Problem 6

asked Feb 14, 2023 at 21:11

5 votes

1 answer

540 views

Is my proof that "Two lines perpendicular to the same line are parallel" correct?

asked Oct 31, 2022 at 14:38

5 votes

3 answers

512 views

Approximate $\int_0^\pi e^{e^x} dx$

asked Nov 16, 2022 at 21:21

5 votes

2 answers

266 views

Calculate $\int_0^1 \ln^{2020}(x)dx$

asked Nov 17, 2022 at 19:05

5 votes

2 answers

261 views

How to calculate $\int_{-\infty}^\infty\frac{e^x}{1+e^{3x}}dx$ using residues [duplicate]

asked Jan 19 at 16:02

5 votes

1 answer

93 views

Prove that $\lim_{x\to-\infty}\left(\psi(x)-\psi\left(\frac x2\right)-\frac1x-\ln 2\right)\sin(\pi x)=\pi$

asked Feb 8 at 3:30

5 votes

2 answers

564 views

MIT Integration bee 2023 Regular Season $\int_0^\pi x\sin^4(x)dx$

asked Feb 16, 2023 at 0:02

4 votes

0 answers

168 views

On the irrationality of $\zeta(\frac{3}{2})$

asked Feb 21, 2023 at 17:10

4 votes

0 answers

242 views

Why does $x+\tan x$ satisfy Glasser's master theorem?

asked May 16, 2023 at 19:18

4 votes

2 answers

200 views

Solving $\int_1^3\frac{1+\frac{1+...}{x+...}}{x+\frac{1+...}{x+...}}dx$

asked Feb 17 at 21:13

4 votes

3 answers

182 views

Find $f(x)$ such that $f(x^2)=f(x)+1$

asked Nov 10, 2023 at 19:14

4 votes

2 answers

94 views

$\int_0^x\frac{\lfloor t\rfloor}{t^2}dt=H_x$ isn't true?

asked Dec 11, 2023 at 21:46

4 votes

1 answer

112 views

Prove that the limit converges to $\gamma$

asked Jan 2, 2023 at 22:47

3 votes

0 answers

202 views

Why is it not known that $\sum_{n>0}\frac{(-1)^nn}{p_n}$ converges?

asked Dec 16, 2022 at 4:55

3 votes

1 answer

669 views

Closed form expression of $\Gamma(\frac{5}{3})$

asked Jan 17, 2023 at 20:43

3 votes

2 answers

115 views

Approximation of $\sum_{k=1}^\infty \frac{1}{T_k}$ where $T_k$ are the tribonacci numbers

asked Dec 5, 2022 at 0:39

3 votes

2 answers

268 views

Is the number satisfying $\eta=\sin(\cos(\eta))$ transcendental?

asked Nov 4, 2022 at 18:28

3 votes

1 answer

158 views

Is this formula new and useful? [duplicate]

asked Sep 13, 2022 at 20:07

3 votes

2 answers

169 views

Prove that $\lim_{n\rightarrow\infty}\frac{f(n)}{n!}=e$

asked Sep 2, 2023 at 23:43

3 votes

4 answers

292 views

Proving $\int_0^\infty\frac1{1+e^{px}}dx=\frac{\ln2}p$

asked Jan 26 at 16:19

Stack Exchange Network

148 Questions

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

Approximating cube roots to high precision.

Solve $\int_0^\infty\frac x{e^x-e^{\frac x2}}dx$

Proving that $\lim_{x\rightarrow0}\frac{H_x}x=\frac{\pi^2}6$

Find $f(x)$ such that $\sum_{k=0}^{\infty}f^k\left(x\right)=\sum_{k=0}^{\infty}f^{\left(k\right)}\left(x\right)$

Is $\sum_{k=1}^\infty \frac{1}{p_{p_k}}$, where $p_k$ is the $k$-th prime, irrational? transcendental?

Proof of $\int_0^1\ln\left(\frac{1}{\ln \frac{1}{x}}\right)dx=\gamma$

Calculate $\int_{-\infty}^\infty\frac{x^2}{1+x^8}dx$

Imaginary numbers and partial fraction decomposition in integration

How to find $\int_0^\infty\frac{x!}{x^x}dx$

2023 MIT Integration Bee Regular Season Problem 6

Is my proof that "Two lines perpendicular to the same line are parallel" correct?

Approximate $\int_0^\pi e^{e^x} dx$

Calculate $\int_0^1 \ln^{2020}(x)dx$

How to calculate $\int_{-\infty}^\infty\frac{e^x}{1+e^{3x}}dx$ using residues [duplicate]

Prove that $\lim_{x\to-\infty}\left(\psi(x)-\psi\left(\frac x2\right)-\frac1x-\ln 2\right)\sin(\pi x)=\pi$

MIT Integration bee 2023 Regular Season $\int_0^\pi x\sin^4(x)dx$

On the irrationality of $\zeta(\frac{3}{2})$

Why does $x+\tan x$ satisfy Glasser's master theorem?

Solving $\int_1^3\frac{1+\frac{1+...}{x+...}}{x+\frac{1+...}{x+...}}dx$

Find $f(x)$ such that $f(x^2)=f(x)+1$

$\int_0^x\frac{\lfloor t\rfloor}{t^2}dt=H_x$ isn't true?

Prove that the limit converges to $\gamma$

Why is it not known that $\sum_{n>0}\frac{(-1)^nn}{p_n}$ converges?

Closed form expression of $\Gamma(\frac{5}{3})$

Approximation of $\sum_{k=1}^\infty \frac{1}{T_k}$ where $T_k$ are the tribonacci numbers

Is the number satisfying $\eta=\sin(\cos(\eta))$ transcendental?

Is this formula new and useful? [duplicate]

Prove that $\lim_{n\rightarrow\infty}\frac{f(n)}{n!}=e$

Proving $\int_0^\infty\frac1{1+e^{px}}dx=\frac{\ln2}p$