Question

Testing for convergence - $\int_{0}^{\infty} \frac{x^4}{e^{\sqrt{x}}} dx$

score 92 · Answer 1 · 2026-04-14 19:41:04

92

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Testing for convergence - $\int_{0}^{\infty} \frac{x^4}{e^{\sqrt{x}}} dx$

Published on 14 Apr 2026 - 19:41

score 203 · Answer 2 · 2026-04-13 10:29:21

203

Views

Integral containing floor function and derivative

Published on 13 Apr 2026 - 10:29

score 251 · Answer 3 · 2026-04-16 08:08:18

251

Views

Show that $\int_{-\infty}^\infty \frac{e^x}{e^{2x}+e^{2a}}\frac{1}{x^2+\pi^2}dx = \frac{2\pi e^{-a}}{4a^2+\pi^2}-\frac{1}{1+e^{2a}}$

Published on 16 Apr 2026 - 8:08

score 170 · Answer 4 · 2026-04-17 03:56:04

170

Views

Show that $ \int_0^{\pi\over 2}\frac{\sin(2nx)}{\sin^{2n+2}(x)}\frac{1}{e^{2\pi \cot x}-1}dx =(-1)^{n-1}\frac{2n-1}{4(2n+1)} $

Published on 17 Apr 2026 - 3:56

score 41 · Answer 5 · 2026-04-15 19:23:23

41

Views

Difference in way of taking limit of improper integral

Published on 15 Apr 2026 - 19:23

score 109 · Answer 6 · 2026-04-17 09:25:34

109

Views

$ \int_0^1(\ln\left(\frac{1}{x}\right))^n $ dx

Published on 17 Apr 2026 - 9:25

score 155 · Answer 7 · 2026-04-16 19:01:52

155

Views

Show that $\int_{0}^{\infty}\sin\left(\frac{1}{x^{2}}\right)\ln xdx=\sqrt{\frac{\pi}{2}}\left(\frac{\gamma}{2}+\frac{\pi}{4}+\ln2-1\right)$

Published on 16 Apr 2026 - 19:01

score 105 · Answer 8 · 2026-04-15 00:13:55

105

Views

What are the conditions on $a$ and $b$ so that the integral converges?

Published on 15 Apr 2026 - 0:13

score 137 · Answer 9 · 2026-04-16 17:51:50

137

Views

Improper Integral $\int_{0}^{\infty} \log(t) t^{-\frac{1}{2}} \exp\left\{-t\right\} dt$

Published on 16 Apr 2026 - 17:51

score 87 · Answer 10 · 2026-03-26 01:01:16

87

Views

How to evaluate this by contour integral?

Published on 26 Mar 2026 - 1:01

score 87 · Answer 11 · 2026-04-17 00:25:57

87

Views

Computing $\int_{e^\pi}^\infty\frac{\sin(\ln(x))dx}{x}$

Published on 17 Apr 2026 - 0:25

score 53 · Answer 12 · 2026-04-17 14:19:06

53

Views

Justifying the existence of an improper integral

Published on 17 Apr 2026 - 14:19

score 138 · Answer 13 · 2026-04-26 03:20:40

138

Views

Frullani's integral

Published on 26 Apr 2026 - 3:20

score 153 · Answer 14 · 2026-04-13 02:37:08

153

Views

Jeffrey's integrals

Published on 13 Apr 2026 - 2:37

score 102 · Answer 15 · 2026-04-16 09:23:07

102

Views

Glitch in computing $\int_0^8\frac{dx}{\sqrt[3]x}$?

Published on 16 Apr 2026 - 9:23

List Question

Testing for convergence - $\int_{0}^{\infty} \frac{x^4}{e^{\sqrt{x}}} dx$

Integral containing floor function and derivative

Show that $\int_{-\infty}^\infty \frac{e^x}{e^{2x}+e^{2a}}\frac{1}{x^2+\pi^2}dx = \frac{2\pi e^{-a}}{4a^2+\pi^2}-\frac{1}{1+e^{2a}}$

Show that $ \int_0^{\pi\over 2}\frac{\sin(2nx)}{\sin^{2n+2}(x)}\frac{1}{e^{2\pi \cot x}-1}dx =(-1)^{n-1}\frac{2n-1}{4(2n+1)} $

Difference in way of taking limit of improper integral

$ \int_0^1(\ln\left(\frac{1}{x}\right))^n $ dx

Show that $\int_{0}^{\infty}\sin\left(\frac{1}{x^{2}}\right)\ln xdx=\sqrt{\frac{\pi}{2}}\left(\frac{\gamma}{2}+\frac{\pi}{4}+\ln2-1\right)$

What are the conditions on $a$ and $b$ so that the integral converges?

Improper Integral $\int_{0}^{\infty} \log(t) t^{-\frac{1}{2}} \exp\left\{-t\right\} dt$

How to evaluate this by contour integral?

Computing $\int_{e^\pi}^\infty\frac{\sin(\ln(x))dx}{x}$

Justifying the existence of an improper integral

Frullani's integral

Jeffrey's integrals

Glitch in computing $\int_0^8\frac{dx}{\sqrt[3]x}$?

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