Question

How to evaluate $\sum_{k=2}^\infty (11k + 7)(k+1)\frac{M^{2k+1}}{(M+N)^{2k+4}}$ as a integral?

score 101 · Answer 1 · 2026-04-13 14:19:37

101

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How to evaluate $\sum_{k=2}^\infty (11k + 7)(k+1)\frac{M^{2k+1}}{(M+N)^{2k+4}}$ as a integral?

Published on 13 Apr 2026 - 14:19

score 297 · Answer 2 · 2026-04-24 02:32:34

297

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Derivatives and Integrals of superexponential functions

Published on 24 Apr 2026 - 2:32

score 99 · Answer 3 · 2026-04-16 00:49:19

99

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Functions such that $\lim_{n\to\infty}\frac{1}{n}(f(\frac{x}{n})+f(\frac{2x}{n})+...+f(\frac{nx}{n}))$=$f(x)$

Published on 16 Apr 2026 - 0:49

score 822 · Answer 4 · 2026-04-15 10:46:57

822

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Evaluating $\int\sqrt{1+\sin x}dx$.

Published on 15 Apr 2026 - 10:46

score 151 · Answer 5 · 2026-05-11 06:12:13

151

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Proof for this "Smoothing" lemma

Published on 11 May 2026 - 6:12

score 1.4k · Answer 6 · 2026-04-15 23:11:37

1.4k

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Evaulating the trigonometric integral $\int \frac{1}{(x^2+1)^2} \, dx$

Published on 15 Apr 2026 - 23:11

score 72 · Answer 7 · 2026-05-11 09:35:38

72

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Find $a\in\mathbb{R}$ such that $\int_1^2 \frac 1{|x-a|+1}dx=\ln a+\ln(3-a)$

Published on 11 May 2026 - 9:35

score 526 · Answer 8 · 2026-04-16 07:27:47

526

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if $\left|\frac{g(x)-g(y)}{x-y}\right| \le 1$, Then find Maximum value of $\left|\int_{2}^{10}g(x)dx-8g(a)\right|$

Published on 16 Apr 2026 - 7:27

score 171 · Answer 9 · 2026-04-12 04:57:31

171

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$L^2$-valued integral as parameter integral

Published on 12 Apr 2026 - 4:57

score 565 · Answer 10 · 2026-04-14 19:06:25

565

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How to show that $uv \le \frac {u^p}{p}+ \frac {v^q}{q}$ where $\frac 1p + \frac 1q = 1$

Published on 14 Apr 2026 - 19:06

score 49 · Answer 11 · 2026-04-13 08:07:22

49

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Integrate a chain function

Published on 13 Apr 2026 - 8:07

score 236 · Answer 12 · 2026-05-10 15:25:38

236

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Integral inequality $\frac{1}{2M}\le\int_0^1xf(x)dx\le1-\frac{1}{2M}$

Published on 10 May 2026 - 15:25

score 302 · Answer 13 · 2026-04-14 15:10:05

302

Views

Establishing an identity between $e^{-x}$ and $e^{-x^2}$ using the Fourier transform.

Published on 14 Apr 2026 - 15:10

score 327 · Answer 14 · 2026-04-15 18:36:35

327

Views

How to evaluate this integral $\int_0^1 \frac{x\log ^2(\sqrt{x^2+1}+1)}{\sqrt{1-x^2}} \, dx$

Published on 15 Apr 2026 - 18:36

score 43 · Answer 15 · 2026-05-10 15:41:09

43

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Multivariable Calculus: Stokes Theorem

Published on 10 May 2026 - 15:41

List Question

How to evaluate $\sum_{k=2}^\infty (11k + 7)(k+1)\frac{M^{2k+1}}{(M+N)^{2k+4}}$ as a integral?

Derivatives and Integrals of superexponential functions

Functions such that $\lim_{n\to\infty}\frac{1}{n}(f(\frac{x}{n})+f(\frac{2x}{n})+...+f(\frac{nx}{n}))$=$f(x)$

Evaluating $\int\sqrt{1+\sin x}dx$.

Proof for this "Smoothing" lemma

Evaulating the trigonometric integral $\int \frac{1}{(x^2+1)^2} \, dx$

Find $a\in\mathbb{R}$ such that $\int_1^2 \frac 1{|x-a|+1}dx=\ln a+\ln(3-a)$

if $\left|\frac{g(x)-g(y)}{x-y}\right| \le 1$, Then find Maximum value of $\left|\int_{2}^{10}g(x)dx-8g(a)\right|$

$L^2$-valued integral as parameter integral

How to show that $uv \le \frac {u^p}{p}+ \frac {v^q}{q}$ where $\frac 1p + \frac 1q = 1$

Integrate a chain function

Integral inequality $\frac{1}{2M}\le\int_0^1xf(x)dx\le1-\frac{1}{2M}$

Establishing an identity between $e^{-x}$ and $e^{-x^2}$ using the Fourier transform.

How to evaluate this integral $\int_0^1 \frac{x\log ^2(\sqrt{x^2+1}+1)}{\sqrt{1-x^2}} \, dx$

Multivariable Calculus: Stokes Theorem

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