Question

The entry-level PhD integral: $\int_0^\infty\frac{\sin 3x\sin 4x\sin5x\cos6x}{x\sin^2 x\cosh x}\ dx$

score 4.2k · Answer 1 · 2016-07-18 18:11:40

4.2k

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The entry-level PhD integral: $\int_0^\infty\frac{\sin 3x\sin 4x\sin5x\cos6x}{x\sin^2 x\cosh x}\ dx$

Published on 18 Jul 2016 - 18:11

score 381 · Answer 2 · 2016-07-19 09:44:06

381

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Closed form of $\int_0^1 \tan(\gamma\sqrt{1-x^2}) dx$

Published on 19 Jul 2016 - 9:44

score 3.1k · Answer 3 · 2016-07-19 22:06:55

3.1k

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A question on the Laplace Transform of $f(t)=t e^{at}\sin (bt)$

Published on 19 Jul 2016 - 22:06

score 201 · Answer 4 · 2016-07-21 02:18:58

201

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Sum $\sum\limits_{j=k}^n\binom{j}{k}(-1)^j$

Published on 21 Jul 2016 - 2:18

score 1.8k · Answer 5 · 2016-07-21 14:18:52

1.8k

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Closed form for $\sum_{n=1}^{\infty}\frac{1}{\sinh^2\!\pi n}$ conjectured

Published on 21 Jul 2016 - 14:18

score 298 · Answer 6 · 2016-07-21 16:43:56

298

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Another way to evaluate $\int\frac{\cos5x+\cos4x}{1-2\cos3x}{dx}$?

Published on 21 Jul 2016 - 16:43

score 270 · Answer 7 · 2026-03-25 16:13:55

270

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How do we show that $\ln{2}-\gamma=\sum_{n=1}^{\infty}{\zeta(2n+1)\over 2^{2n}(2n+1)}?$

Published on 25 Mar 2026 - 16:13

score 132 · Answer 8 · 2016-07-22 00:22:38

132

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Maxwellian integral : is there a closed form?

Published on 22 Jul 2016 - 0:22

score 156 · Answer 9 · 2016-07-22 14:50:46

156

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Proportionally Distributing $N$ items across $B$ bins.

Published on 22 Jul 2016 - 14:50

score 366 · Answer 10 · 2016-07-22 17:00:29

366

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Value of this convergent series: $\frac{1}{3!}+\frac2{5!}+\frac3{7!}+\frac{4}{9!}+\cdots$

Published on 22 Jul 2016 - 17:00

score 559 · Answer 11 · 2026-03-26 07:57:13

559

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Path length of Gaussian

Published on 26 Mar 2026 - 7:57

score 1.4k · Answer 12 · 2016-07-23 16:07:21

1.4k

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Trigonometry Olympiad problem: Evaluate $1\sin 2^{\circ} +2\sin 4^{\circ} + 3\sin 6^{\circ}+\cdots+ 90\sin180^{\circ}$

Published on 23 Jul 2016 - 16:07

score 241 · Answer 13 · 2016-07-25 13:25:59

241

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Sum to infinity of trignometry inverse: $\sum_{r=1}^\infty\arctan \left(\frac{4}{r^2+3} \right)$

Published on 25 Jul 2016 - 13:25

score 913 · Answer 14 · 2026-03-25 23:09:01

913

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Formula for number of faces in 4 dimensions

Published on 25 Mar 2026 - 23:09

score 142 · Answer 15 · 2016-07-26 06:04:54

142

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Solving an equation involving an integral: $\int_0^1\frac{ax+b}{(x^2+3x+2)^2}\:dx=\frac52.$

Published on 26 Jul 2016 - 6:04

List Question

The entry-level PhD integral: $\int_0^\infty\frac{\sin 3x\sin 4x\sin5x\cos6x}{x\sin^2 x\cosh x}\ dx$

Closed form of $\int_0^1 \tan(\gamma\sqrt{1-x^2}) dx$

A question on the Laplace Transform of $f(t)=t e^{at}\sin (bt)$

Sum $\sum\limits_{j=k}^n\binom{j}{k}(-1)^j$

Closed form for $\sum_{n=1}^{\infty}\frac{1}{\sinh^2\!\pi n}$ conjectured

Another way to evaluate $\int\frac{\cos5x+\cos4x}{1-2\cos3x}{dx}$?

How do we show that $\ln{2}-\gamma=\sum_{n=1}^{\infty}{\zeta(2n+1)\over 2^{2n}(2n+1)}?$

Maxwellian integral : is there a closed form?

Proportionally Distributing $N$ items across $B$ bins.

Value of this convergent series: $\frac{1}{3!}+\frac2{5!}+\frac3{7!}+\frac{4}{9!}+\cdots$

Path length of Gaussian

Trigonometry Olympiad problem: Evaluate $1\sin 2^{\circ} +2\sin 4^{\circ} + 3\sin 6^{\circ}+\cdots+ 90\sin180^{\circ}$

Sum to infinity of trignometry inverse: $\sum_{r=1}^\infty\arctan \left(\frac{4}{r^2+3} \right)$

Formula for number of faces in 4 dimensions

Solving an equation involving an integral: $\int_0^1\frac{ax+b}{(x^2+3x+2)^2}\:dx=\frac52.$

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