List questions from improper-integrals

Published on 04 Jun 2020 - 17:47

86

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Computing $\int_{\textbf{R}^n} \langle x,a \rangle ^2 e^{-\frac{1}{2} \|x\| ^2}$ for some $a\in \textbf{R}^n$.

Published on 04 Jun 2020 - 21:01

202

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Evaluating the following integral $\int_{0}^{\infty} \frac{\ln(x^{2}+1)} {(x(x^{2}+1))} dx$

Published on 25 Mar 2026 - 3:21

41

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How would I go about showing the following result to be true using contour integration?

Published on 06 Apr 2026 - 6:18

77

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Asymptotics of $\int_1^{\infty}\frac{f(x)}{x-1-iy}\,\mathrm{d}x$ as $y\to0$

Published on 07 Jun 2020 - 18:16

153

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Evaluating $\int_{0}^{\infty} (\frac{\sin x}{x})^2 dx$ using complex analysis

Published on 07 Jun 2020 - 21:31

41

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Finding indefinite integration to work with Fundamental Theorem of Calculus

Published on 08 Jun 2020 - 7:36

63

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Connection of branches

Published on 02 Apr 2026 - 2:56

86

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Calculating $\int_A \frac{z}{y^2}$ with $A:=\{z\ge0,x\ge1,y\ge 0, x^2+z^2<\min(2x,y^2)\}$

Published on 28 Mar 2026 - 11:48

86

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Integral $\int_{0}^{1} \dfrac{\ln(1-x)}{x}~dx$

Published on 09 Jun 2020 - 1:48

1.2k

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Mean value theorem for Improper Integrals

Published on 09 Jun 2020 - 9:29

432

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Solve $\int_{0}^{\infty}\ln\Big(\frac{\sin^2(x)}{x^2}+1\Big)dx=?$

Published on 09 Jun 2020 - 9:34

62

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Improper integral of $\sin(\frac{1}{x})-(\frac{1}{x})\cos(\frac{1}{x})$

Published on 09 Jun 2020 - 13:33

101

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How to show that the beta funcction is well defined?

Published on 26 Mar 2026 - 9:49

26

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finding convergence of integral having exponential and cosine terms

Published on 09 Jun 2020 - 22:41

List Question

Convergence of integral $\int_1^2 \frac{\sqrt{x}} {\ln(x)} \,dx $

Computing $\int_{\textbf{R}^n} \langle x,a \rangle ^2 e^{-\frac{1}{2} \|x\| ^2}$ for some $a\in \textbf{R}^n$.

Evaluating the following integral $\int_{0}^{\infty} \frac{\ln(x^{2}+1)} {(x(x^{2}+1))} dx$

How would I go about showing the following result to be true using contour integration?

Asymptotics of $\int_1^{\infty}\frac{f(x)}{x-1-iy}\,\mathrm{d}x$ as $y\to0$

Evaluating $\int_{0}^{\infty} (\frac{\sin x}{x})^2 dx$ using complex analysis

Finding indefinite integration to work with Fundamental Theorem of Calculus

Connection of branches

Calculating $\int_A \frac{z}{y^2}$ with $A:=\{z\ge0,x\ge1,y\ge 0, x^2+z^2<\min(2x,y^2)\}$

Integral $\int_{0}^{1} \dfrac{\ln(1-x)}{x}~dx$

Mean value theorem for Improper Integrals

Solve $\int_{0}^{\infty}\ln\Big(\frac{\sin^2(x)}{x^2}+1\Big)dx=?$

Improper integral of $\sin(\frac{1}{x})-(\frac{1}{x})\cos(\frac{1}{x})$

How to show that the beta funcction is well defined?

finding convergence of integral having exponential and cosine terms

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