Question

Find $\int\limits^{\infty}_{0}\frac{1}{(x^8+5x^6+14x^4+5x^2+1)^4}dx$

score 354 · Answer 1 · 2016-09-13 16:46:36

354

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Find $\int\limits^{\infty}_{0}\frac{1}{(x^8+5x^6+14x^4+5x^2+1)^4}dx$

Published on 13 Sep 2016 - 16:46

score 260 · Answer 2 · 2016-09-13 18:55:03

260

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How to calculate $\sum_{k=0}^n a^k\sin(kx)$?

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score 229 · Answer 3 · 2026-03-31 08:52:49

229

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Approximation of the factorial function

Published on 31 Mar 2026 - 8:52

score 31 · Answer 4 · 2016-09-14 23:07:44

31

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Finding the closed form ...

Published on 14 Sep 2016 - 23:07

score 1.4k · Answer 5 · 2016-09-15 18:47:44

1.4k

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Prove $\int_0^{\pi/2}{\frac{1+2\cos 2x\cdot\ln\tan x}{1+\tan^{2\sqrt{2}} x}}\tan^{1/\sqrt{2}} x~dx=0$

Published on 15 Sep 2016 - 18:47

score 444 · Answer 6 · 2026-03-27 07:45:52

444

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Closed formula for the sums $\sum\limits_{1 \le i_1 < i_2 < \dots < i_k \le n} i_1 i_2 \cdots i_k $?

Published on 27 Mar 2026 - 7:45

score 94 · Answer 7 · 2016-09-15 23:17:56

94

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How to solve $\lim_{x \to 0} \dfrac{\arctan(x)}{e^{2x}-1}$?

Published on 15 Sep 2016 - 23:17

score 89 · Answer 8 · 2016-09-16 07:53:27

89

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Evaluating the limit of the sequence: $\frac{ 1^a + 2^a +..... n^a}{(n+1)^{a-1}[n^2a + n(n+1)/2]}$

Published on 16 Sep 2016 - 7:53

score 54 · Answer 9 · 2016-09-16 14:21:17

54

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Is there a closed form for the number of ways to put up to $k$ chess pieces on a board with $n$ squares?

Published on 16 Sep 2016 - 14:21

score 71 · Answer 10 · 2026-03-25 13:44:04

71

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Infinite Product for Multiplicative Functions

Published on 25 Mar 2026 - 13:44

score 55 · Answer 11 · 2016-09-18 15:36:23

55

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Proof that recursion $U_0 = 0$, $U_n= 1 + U_\left \lfloor n/2 \right \rfloor$, is solved by $U_n = \left \lfloor \log_2(n) \right \rfloor + 1$

Published on 18 Sep 2016 - 15:36

score 2.1k · Answer 12 · 2026-03-27 06:56:38

2.1k

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How to find the closed formula for $\sum _{i=0}^n {i q^i}$?

Published on 27 Mar 2026 - 6:56

score 821 · Answer 13 · 2016-09-19 17:33:44

821

Views

Solving a recurrence with an alternating pattern e.g. do $\mathrm X$, then do $\mathrm Y$; repeat

Published on 19 Sep 2016 - 17:33

score 196 · Answer 14 · 2016-09-19 21:19:58

196

Views

Closed form for this sum involving the lower incomplete gamma function?

Published on 19 Sep 2016 - 21:19

score 162 · Answer 15 · 2016-09-20 20:35:09

162

Views

Determine sum of the series $\sum_{k=1}^\infty\frac{1}{n(n+1)(n+2)}$

Published on 20 Sep 2016 - 20:35

List Question

Find $\int\limits^{\infty}_{0}\frac{1}{(x^8+5x^6+14x^4+5x^2+1)^4}dx$

How to calculate $\sum_{k=0}^n a^k\sin(kx)$?

Approximation of the factorial function

Finding the closed form ...

Prove $\int_0^{\pi/2}{\frac{1+2\cos 2x\cdot\ln\tan x}{1+\tan^{2\sqrt{2}} x}}\tan^{1/\sqrt{2}} x~dx=0$

Closed formula for the sums $\sum\limits_{1 \le i_1 < i_2 < \dots < i_k \le n} i_1 i_2 \cdots i_k $?

How to solve $\lim_{x \to 0} \dfrac{\arctan(x)}{e^{2x}-1}$?

Evaluating the limit of the sequence: $\frac{ 1^a + 2^a +..... n^a}{(n+1)^{a-1}[n^2a + n(n+1)/2]}$

Is there a closed form for the number of ways to put up to $k$ chess pieces on a board with $n$ squares?

Infinite Product for Multiplicative Functions

Proof that recursion $U_0 = 0$, $U_n= 1 + U_\left \lfloor n/2 \right \rfloor$, is solved by $U_n = \left \lfloor \log_2(n) \right \rfloor + 1$

How to find the closed formula for $\sum _{i=0}^n {i q^i}$?

Solving a recurrence with an alternating pattern e.g. do $\mathrm X$, then do $\mathrm Y$; repeat

Closed form for this sum involving the lower incomplete gamma function?

Determine sum of the series $\sum_{k=1}^\infty\frac{1}{n(n+1)(n+2)}$

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