Question

Integral of Logarithm with complex terms

score 114 · Answer 1 · 2026-04-08 22:25:03

114

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Integral of Logarithm with complex terms

Published on 08 Apr 2026 - 22:25

score 93 · Answer 2 · 2026-03-25 19:51:34

93

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Little integral $\int_{0}^{\infty}\ln\Big(\frac{x^2-2x+1}{x^2+2x+1}\Big)e^{-x}dx$ related to the Gompertz constant

Published on 25 Mar 2026 - 19:51

score 142 · Answer 3 · 2026-04-16 19:49:20

142

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Nice integral $\int_{0}^{\infty}\ln\Big(\frac{x^3-x^2-x+1}{x^3+x^2+x+1}\Big)\frac{1}{x}dx=-\frac{3\pi^2}{4}$

Published on 16 Apr 2026 - 19:49

score 130 · Answer 4 · 2026-04-16 14:34:02

130

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Integrate logarithmic function $\int_0^\infty \frac{\ln(1+25x^2)}{1+16x^2} dx$

Published on 16 Apr 2026 - 14:34

score 32 · Answer 5 · 2026-04-10 17:00:08

32

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How to perform function transformations in a semi-log environment?

Published on 10 Apr 2026 - 17:00

score 28 · Answer 6 · 2026-04-10 11:11:06

28

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Resolve Logarithmic inequation

Published on 10 Apr 2026 - 11:11

score 41 · Answer 7 · 2026-04-13 17:03:02

41

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Can I solve for $\sum_{i=1}^{n}{a_i}$ knowing $\sum_{i=1}^{n}{\ln(a_i)}$?

Published on 13 Apr 2026 - 17:03

score 49 · Answer 8 · 2026-04-16 19:13:07

49

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Finding solution set of $\frac{1}{\log_4 \left(\frac{x+1}{x+2}\right)}<\frac{1}{\log_4(x+3)}$ without using derivatives

Published on 16 Apr 2026 - 19:13

score 122 · Answer 9 · 2026-03-25 19:00:18

122

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Logarithmic derivative of matrix function

Published on 25 Mar 2026 - 19:00

score 59 · Answer 10 · 2026-04-16 02:48:01

59

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Prove that there exists one and only $n\in\mathbb{Z}$ so that $10^{n}\leq x<10^{n+1}$

Published on 16 Apr 2026 - 2:48

score 398 · Answer 11 · 2026-04-13 04:42:50

398

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Simplifying $\exp(a)\ln(b)$

Published on 13 Apr 2026 - 4:42

score 72 · Answer 12 · 2026-04-14 22:47:04

72

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Studying the equation $\ln(x)- 1+ x^2=0$

Published on 14 Apr 2026 - 22:47

score 96 · Answer 13 · 2026-04-15 21:01:27

96

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How to solve $\ln{x}+1−x^2=0$?

Published on 15 Apr 2026 - 21:01

score 214 · Answer 14 · 2026-04-17 00:44:24

214

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Finding $\lambda$ such that $(\ln(x^2-2x+2))^2+\lambda \ln(x^2-2x+2)+1\gt 0 \forall x\gt 1$

Published on 17 Apr 2026 - 0:44

score 22 · Answer 15 · 2026-03-26 19:25:06

22

Views

Can function $\log (-\log \left| x\right| )$ be approximated by a logarithmic function at zero?

Published on 26 Mar 2026 - 19:25

List Question

Integral of Logarithm with complex terms

Little integral $\int_{0}^{\infty}\ln\Big(\frac{x^2-2x+1}{x^2+2x+1}\Big)e^{-x}dx$ related to the Gompertz constant

Nice integral $\int_{0}^{\infty}\ln\Big(\frac{x^3-x^2-x+1}{x^3+x^2+x+1}\Big)\frac{1}{x}dx=-\frac{3\pi^2}{4}$

Integrate logarithmic function $\int_0^\infty \frac{\ln(1+25x^2)}{1+16x^2} dx$

How to perform function transformations in a semi-log environment?

Resolve Logarithmic inequation

Can I solve for $\sum_{i=1}^{n}{a_i}$ knowing $\sum_{i=1}^{n}{\ln(a_i)}$?

Finding solution set of $\frac{1}{\log_4 \left(\frac{x+1}{x+2}\right)}<\frac{1}{\log_4(x+3)}$ without using derivatives

Logarithmic derivative of matrix function

Prove that there exists one and only $n\in\mathbb{Z}$ so that $10^{n}\leq x<10^{n+1}$

Simplifying $\exp(a)\ln(b)$

Studying the equation $\ln(x)- 1+ x^2=0$

How to solve $\ln{x}+1−x^2=0$?

Finding $\lambda$ such that $(\ln(x^2-2x+2))^2+\lambda \ln(x^2-2x+2)+1\gt 0 \forall x\gt 1$

Can function $\log (-\log \left| x\right| )$ be approximated by a logarithmic function at zero?

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