User user85798

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user85798

Member for 10 years, 4 months
Last seen more than 5 years ago

162 Questions

Score Activity Newest Views

51 votes

9 answers

98k views

What is the difference between an indefinite integral and an antiderivative?

asked Nov 29, 2013 at 21:11

38 votes

5 answers

5k views

Integrate $\int_0^{\pi/2} \frac{1}{1+\tan^\alpha{x}}\,\mathrm{d}x$

asked Dec 13, 2013 at 17:24

37 votes

4 answers

41k views

The set of real numbers and power set of the natural numbers

asked Nov 5, 2013 at 22:42

28 votes

3 answers

5k views

Fibonacci numbers that are powers of 2

asked May 15, 2014 at 10:56

27 votes

1 answer

872 views

Prove $\int_{0}^\infty \frac{1}{\Gamma(x)}\, \mathrm{d}x = e + \int_0^\infty \frac{e^{-x}}{\pi^2 + \ln^2 x}\, \mathrm{d}x$

asked Apr 5, 2014 at 16:28

18 votes

1 answer

1k views

Evaluating $\int_0^\infty \frac {\cos {\pi x}} {e^{2\pi \sqrt x} - 1} \mathrm d x$

asked May 18, 2014 at 15:21

18 votes

3 answers

9k views

Infinite sets with cardinality less than the natural numbers

asked Oct 30, 2013 at 7:58

16 votes

4 answers

5k views

Proof that one large number is larger than another large number

asked Nov 1, 2013 at 14:57

12 votes

4 answers

373 views

Definite Integral $\int_0^1\frac{\ln(x^2-x+1)}{x^2-x}\,\mathrm{d}x$

asked Feb 26, 2014 at 9:27

12 votes

1 answer

823 views

Evaluate $\int_0^{\pi/4} \frac {\sin x} {x \cos^2 x} \mathrm d x$

asked Apr 28, 2014 at 19:13

12 votes

5 answers

737 views

Evaluating $\int_0^{\infty} \frac {e^{-x}}{a^2 + \log^2 x}\, \mathrm d x$

asked Nov 25, 2015 at 10:41

12 votes

3 answers

160 views

Showing $8.9<\int_3^5 \sqrt{4+x^2} \, \mathrm d x < 9$

asked Feb 22, 2018 at 11:15

11 votes

2 answers

778 views

Weird limit $\lim \limits_{n\mathop\to\infty}\frac{1}{e^n}\sum \limits_{k\mathop=0}^n\frac{n^k}{k!} $ [duplicate]

asked Mar 31, 2014 at 9:24

10 votes

1 answer

721 views

Integrate $\frac{5x^3 +2}{\sqrt{x^3+1}}$

asked Sep 20, 2013 at 0:51

9 votes

4 answers

493 views

Evaluate a finite sum with four factorials

asked Feb 22, 2014 at 20:20

9 votes

1 answer

296 views

Infinite series

asked Dec 20, 2013 at 7:03

9 votes

1 answer

5k views

Proving that I can interchange limit and infinite sum

asked Oct 25, 2015 at 2:07

9 votes

1 answer

6k views

How to show two infinite-dimensional vector spaces are not isomorphic

asked Oct 26, 2015 at 19:16

9 votes

2 answers

1k views

Is there only one way to make $\mathbb R^2$ a field?

asked Jan 25, 2016 at 21:37

8 votes

1 answer

1k views

Is the Mandelbrot set path-connected?

asked Jan 26, 2018 at 17:28

8 votes

4 answers

5k views

Let $a, b, c$ be positive real numbers such that $abc = 1$. Prove that $a^2 + b^2 + c^2 \ge a + b + c$.

asked Nov 26, 2013 at 15:07

8 votes

2 answers

304 views

$A_1 \cap A_2 \cap \cdots \cap A_n \ne \emptyset$ holds for all $n$. Must it be that $\bigcap_{n = 1}^{\infty} A_n \ne \emptyset$?

asked Oct 17, 2014 at 15:31

7 votes

2 answers

2k views

Taylor Series of $\tan x$

asked Apr 26, 2014 at 16:04

7 votes

1 answer

242 views

What is wrong with sets like $\{a,\{a\},\{\{a\}\},\ldots\}$

asked Dec 9, 2015 at 4:56

7 votes

3 answers

311 views

Easy question that I can't do: Find all continuous functions satisfying $\left\|\int_0^1 f\right\|= \int_0^1 \|f\|$

asked Nov 9, 2015 at 11:35

7 votes

2 answers

171 views

Evaluating $\oint_{|z|=2} \frac{\log{(z-\alpha)}}{z}-\frac{\log z}z \, \mathrm dz$

asked May 25, 2018 at 2:00

6 votes

1 answer

506 views

Classifying singularities of $\frac {z^{1/2}-1}{\sin{\pi z}}$

asked May 23, 2018 at 12:12

6 votes

1 answer

455 views

Proving $\lim_{n \to \infty} \frac {\log{p_n}} {\log n} = 1$

asked Dec 13, 2015 at 14:34

6 votes

1 answer

2k views

Group of order $60$ with more than one Sylow-$5$ subgroup is simple

asked Feb 8, 2018 at 1:28

6 votes

1 answer

149 views

Evaluating $\lim\limits_{x\mathop\to\infty}\frac{\tan x}{x}$

asked Apr 12, 2014 at 22:52

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