Question

Show that $\int_0^1(\ln\Gamma)(x)\mathrm dx=\ln(\sqrt{2\pi})$

score 361 · Answer 1 · 2026-04-16 00:08:09

361

Views

Show that $\int_0^1(\ln\Gamma)(x)\mathrm dx=\ln(\sqrt{2\pi})$

Published on 16 Apr 2026 - 0:08

score 115 · Answer 2 · 2026-04-12 15:58:43

115

Views

How to evaluate this integral ?

Published on 12 Apr 2026 - 15:58

score 872 · Answer 3 · 2026-04-15 17:11:25

872

Views

Calculate $\int_{-\infty}^{+\infty}\frac{x}{1+x^2}dx$, what is wrong with this?

Published on 15 Apr 2026 - 17:11

score 67 · Answer 4 · 2026-04-15 19:46:21

67

Views

Study the convergence of $ \int_{3}^{+\infty} \sin\left(\frac{1}{x}\right)- \tan\left(\frac{1}{x}\right)\, dx $

Published on 15 Apr 2026 - 19:46

score 480 · Answer 5 · 2026-04-12 05:52:56

480

Views

Solving Exponential integral with Numerical Integration

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score 88 · Answer 6 · 2026-04-12 07:49:35

88

Views

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Published on 12 Apr 2026 - 7:49

score 377 · Answer 7 · 2026-04-15 14:24:52

377

Views

How do I Evaluate the Integral $\int_{-\infty }^{\infty } \frac{1}{e^{x^2}+1} \, dx$?

Published on 15 Apr 2026 - 14:24

score 634 · Answer 8 · 2026-04-16 04:37:40

634

Views

$\int_{-1}^0 \frac{(e^{1/x})}{x^2}\ dx$ Improper integrals

Published on 16 Apr 2026 - 4:37

score 152 · Answer 9 · 2026-04-11 00:16:43

152

Views

Question about the limit comparison test (for improper integrals) and intuition

Published on 11 Apr 2026 - 0:16

score 257 · Answer 10 · 2026-04-11 22:20:49

257

Views

double integration involving infinity

Published on 11 Apr 2026 - 22:20

score 194 · Answer 11 · 2026-04-16 02:12:19

194

Views

Show that $\int_{-\infty}^{+\infty}\left|\frac{\sin x}{x}\right|\mathrm dx$ diverges to infinity

Published on 16 Apr 2026 - 2:12

score 112 · Answer 12 · 2026-04-17 05:29:30

Proving the inequality $0\leq \frac{\sqrt{xy}}{1-p}\frac{x^{\frac{1}{p}-1}-y^{\frac{1}{p}-1}}{x^{\frac{1}{p}}-y^{\frac{1}{p}}} \leq 1$

score 87 · Answer 13 · 2026-04-11 14:32:48

87

Views

improper integral convergence

Published on 11 Apr 2026 - 14:32

score 178 · Answer 14 · 2026-04-16 03:59:59

178

Views

Why does the integral $\int_1^\infty\frac{\sin(x)}{x^2}dx$ exist?

Published on 16 Apr 2026 - 3:59

score 155 · Answer 15 · 2026-04-13 01:46:36

155

Views

Differential entropy of Gaussian kernel density estimator?

Published on 13 Apr 2026 - 1:46

List Question

Show that $\int_0^1(\ln\Gamma)(x)\mathrm dx=\ln(\sqrt{2\pi})$

How to evaluate this integral ?

Calculate $\int_{-\infty}^{+\infty}\frac{x}{1+x^2}dx$, what is wrong with this?

Study the convergence of $ \int_{3}^{+\infty} \sin\left(\frac{1}{x}\right)- \tan\left(\frac{1}{x}\right)\, dx $

Solving Exponential integral with Numerical Integration

double integral to simple integral

How do I Evaluate the Integral $\int_{-\infty }^{\infty } \frac{1}{e^{x^2}+1} \, dx$?

$\int_{-1}^0 \frac{(e^{1/x})}{x^2}\ dx$ Improper integrals

Question about the limit comparison test (for improper integrals) and intuition

double integration involving infinity

Show that $\int_{-\infty}^{+\infty}\left|\frac{\sin x}{x}\right|\mathrm dx$ diverges to infinity

Proving the inequality $0\leq \frac{\sqrt{xy}}{1-p}\frac{x^{\frac{1}{p}-1}-y^{\frac{1}{p}-1}}{x^{\frac{1}{p}}-y^{\frac{1}{p}}} \leq 1$

improper integral convergence

Why does the integral $\int_1^\infty\frac{\sin(x)}{x^2}dx$ exist?

Differential entropy of Gaussian kernel density estimator?

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