Question

Evaluate $\int_0^\infty \frac{\arctan(3x) - \arctan(9x)}{x} {dx}$

score 744 · Answer 1 · 2014-11-14 10:02:47

744

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Evaluate $\int_0^\infty \frac{\arctan(3x) - \arctan(9x)}{x} {dx}$

Published on 14 Nov 2014 - 10:02

score 75 · Answer 2 · 2014-11-14 17:45:31

75

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The limit of $ m\int_{a}^{1/m} \frac{dx}{x}=0 $ and $ m\int_{a}^{\infty} \frac{dx}{x^{1+m}}=0$ as $m\to0$

Published on 14 Nov 2014 - 17:45

score 57 · Answer 3 · 2014-11-15 16:11:04

57

Views

How do I manipulate orders of integration to cancel out a nested integral leaving me with only 1?

Published on 15 Nov 2014 - 16:11

score 49 · Answer 4 · 2014-11-15 18:44:18

49

Views

Behavior of Improper Integral

Published on 15 Nov 2014 - 18:44

score 192 · Answer 5 · 2014-11-16 02:48:40

192

Views

Why does an improper integral turn into an answer with factorial?

Published on 16 Nov 2014 - 2:48

score 266 · Answer 6 · 2026-03-29 10:27:39

266

Views

Evaluating $I_{\alpha}=\int_{0}^{\infty} \frac{\ln(1+x^2)}{x^\alpha}dx$ using complex analysis

Published on 29 Mar 2026 - 10:27

score 613 · Answer 7 · 2014-11-17 12:54:07

613

Views

Example of a function $f(x)$ such that the integral of $f(x^2)$ converges but the integral of $f(x)$ diverges?

Published on 17 Nov 2014 - 12:54

score 55 · Answer 8 · 2026-03-28 22:13:46

55

Views

Limit of an integral that arose in Fourier Analysis

Published on 28 Mar 2026 - 22:13

score 96 · Answer 9 · 2026-04-02 07:21:39

96

Views

Integration of $\exp[f(x,y)]$

Published on 02 Apr 2026 - 7:21

score 196 · Answer 10 · 2014-11-19 13:01:57

196

Views

How to evaluate if $\int_2^\infty {\frac{1}{\log(x)\cdot \sqrt{x^2+1}}}dx$ converges?

Published on 19 Nov 2014 - 13:01

score 1.4k · Answer 11 · 2026-04-04 00:13:50

1.4k

Views

Evaluating $\int_0^{\infty} \frac{\sqrt{x}}{x^2+2x+5} dx$ using complex analysis

Published on 04 Apr 2026 - 0:13

score 97 · Answer 12 · 2014-11-19 18:44:20

97

Views

What am I doing with this triple integral?

Published on 19 Nov 2014 - 18:44

score 189 · Answer 13 · 2014-11-19 20:12:22

189

Views

Closed form for $\int_0^\infty e^{-x}\sin^a(x)dx$

Published on 19 Nov 2014 - 20:12

score 1.5k · Answer 14 · 2014-11-20 04:21:28

1.5k

Views

Evaluate $\int_0^1 \frac{x^k-1}{\ln x}dx $ using high school techniques

Published on 20 Nov 2014 - 4:21

score 86 · Answer 15 · 2014-11-21 00:25:51

86

Views

Improper integral of $\int\frac{2}{x^2-1}$

Published on 21 Nov 2014 - 0:25

List Question

Evaluate $\int_0^\infty \frac{\arctan(3x) - \arctan(9x)}{x} {dx}$

The limit of $ m\int_{a}^{1/m} \frac{dx}{x}=0 $ and $ m\int_{a}^{\infty} \frac{dx}{x^{1+m}}=0$ as $m\to0$

How do I manipulate orders of integration to cancel out a nested integral leaving me with only 1?

Behavior of Improper Integral

Why does an improper integral turn into an answer with factorial?

Evaluating $I_{\alpha}=\int_{0}^{\infty} \frac{\ln(1+x^2)}{x^\alpha}dx$ using complex analysis

Example of a function $f(x)$ such that the integral of $f(x^2)$ converges but the integral of $f(x)$ diverges?

Limit of an integral that arose in Fourier Analysis

Integration of $\exp[f(x,y)]$

How to evaluate if $\int_2^\infty {\frac{1}{\log(x)\cdot \sqrt{x^2+1}}}dx$ converges?

Evaluating $\int_0^{\infty} \frac{\sqrt{x}}{x^2+2x+5} dx$ using complex analysis

What am I doing with this triple integral?

Closed form for $\int_0^\infty e^{-x}\sin^a(x)dx$

Evaluate $\int_0^1 \frac{x^k-1}{\ln x}dx $ using high school techniques

Improper integral of $\int\frac{2}{x^2-1}$

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