Question

How to generalize this problem for powers of sine function?

score 120 · Answer 1 · 2026-04-09 10:17:15

120

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How to generalize this problem for powers of sine function?

Published on 09 Apr 2026 - 10:17

score 212 · Answer 2 · 2026-04-15 22:05:06

212

Views

Does $\int_{-\infty}^{\infty}\sin^{-1}\left(\frac{\sin(x)}{x}\right)dx$ converge?

Published on 15 Apr 2026 - 22:05

score 224 · Answer 3 · 2026-04-17 13:47:21

224

Views

Evaluate $\int_{-\infty}^{\infty}\sin^{-1}\left(\frac{\sin(x)}{x}\right)dx$

Published on 17 Apr 2026 - 13:47

score 140 · Answer 4 · 2026-03-25 21:48:49

140

Views

Does $\displaystyle\lim\limits_{a\to\infty}\frac{1}{a}\int\limits_{-\infty}^{a}\{e^x\}dx=\frac{1}{2}$?

Published on 25 Mar 2026 - 21:48

score 196 · Answer 5 · 2026-04-16 11:31:45

196

Views

Does $\int_{-\infty}^{\infty}\ln\left(e^{-x^{2}}+1\right)dx=\frac{3\pi}{4}-1$?

Published on 16 Apr 2026 - 11:31

score 100 · Answer 6 · 2026-04-15 05:53:40

100

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What methods can be used to solve $\int_{0}^{\infty}x^{-\ln x}dx=\sqrt{\pi\sqrt{e}}$?

Published on 15 Apr 2026 - 5:53

score 27 · Answer 7 · 2026-04-14 01:42:41

27

Views

Relation between Gaussian integral and Kummer's hypergeometric function

Published on 14 Apr 2026 - 1:42

score 46 · Answer 8 · 2026-04-12 12:15:22

This corollary tells us that any theorem we prove about extended integrals has implications for ordinary integrals. (Munkres Analysis on Manifolds)

score 84 · Answer 9 · 2026-04-16 01:10:26

84

Views

$\sum_{n=1}^{+\infty} \frac{1}{n}\int_{na}^{nb}f(x)dx<+∞$ $\Rightarrow$ $\int_0^{+\infty}f(x)dx$ converges

Published on 16 Apr 2026 - 1:10

score 62 · Answer 10 · 2026-04-17 15:43:12

62

Views

Is there a simple way to evaluate the integral $\int_{\mathbb{R}^n} \delta(x_1^2+\dots+x_n^2-y)\text{d}x_1\dots\text{d}x_n$?

Published on 17 Apr 2026 - 15:43

score 69 · Answer 11 · 2026-04-15 05:29:07

69

Views

Is this Improper Integral Correct?

Published on 15 Apr 2026 - 5:29

score 46 · Answer 12 · 2026-04-11 13:40:42

46

Views

Challenging convergent improper

Published on 11 Apr 2026 - 13:40

score 56 · Answer 13 · 2026-04-14 04:13:44

56

Views

Non-uniform convergence of improper integrals

Published on 14 Apr 2026 - 4:13

score 91 · Answer 14 · 2026-04-15 09:00:16

91

Views

What is $\int_{0}^{\infty}\left(\frac{\pi}{2}-\arctan\left(x^{a}\right)\right)dx$?

Published on 15 Apr 2026 - 9:00

score 154 · Answer 15 · 2026-04-17 03:23:42

154

Views

Integrating $\int_{0}^{1} \left(\frac{\arctan(x) - x}{x^2}\right)^2 \,dx$

Published on 17 Apr 2026 - 3:23

List Question

How to generalize this problem for powers of sine function?

Does $\int_{-\infty}^{\infty}\sin^{-1}\left(\frac{\sin(x)}{x}\right)dx$ converge?

Evaluate $\int_{-\infty}^{\infty}\sin^{-1}\left(\frac{\sin(x)}{x}\right)dx$

Does $\displaystyle\lim\limits_{a\to\infty}\frac{1}{a}\int\limits_{-\infty}^{a}\{e^x\}dx=\frac{1}{2}$?

Does $\int_{-\infty}^{\infty}\ln\left(e^{-x^{2}}+1\right)dx=\frac{3\pi}{4}-1$?

What methods can be used to solve $\int_{0}^{\infty}x^{-\ln x}dx=\sqrt{\pi\sqrt{e}}$?

Relation between Gaussian integral and Kummer's hypergeometric function

This corollary tells us that any theorem we prove about extended integrals has implications for ordinary integrals. (Munkres Analysis on Manifolds)

$\sum_{n=1}^{+\infty} \frac{1}{n}\int_{na}^{nb}f(x)dx<+∞$ $\Rightarrow$ $\int_0^{+\infty}f(x)dx$ converges

Is there a simple way to evaluate the integral $\int_{\mathbb{R}^n} \delta(x_1^2+\dots+x_n^2-y)\text{d}x_1\dots\text{d}x_n$?

Is this Improper Integral Correct?

Challenging convergent improper

Non-uniform convergence of improper integrals

What is $\int_{0}^{\infty}\left(\frac{\pi}{2}-\arctan\left(x^{a}\right)\right)dx$?

Integrating $\int_{0}^{1} \left(\frac{\arctan(x) - x}{x^2}\right)^2 \,dx$

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