List questions from improper-integrals

Published on 16 Apr 2026 - 3:10

42

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Improper integral asymptote shortcut

Published on 12 Apr 2026 - 15:57

79

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Finiteness of the integral of the square of a non-negative continuous unbounded function

Published on 10 Apr 2026 - 5:15

140

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How to find the solution for this integral equation?

Published on 11 Apr 2026 - 2:24

189

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Help with a limit about $F(x) = \displaystyle\int_1^x \frac{ \log t}{(t+a)(t-1)} dt$

Published on 15 Apr 2026 - 17:39

154

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Calculate $I = \int_{0}^{\infty} \int_{0}^{\infty} \frac{\ln(xy)}{(x^2 + x + 1)(y^2 + y + 1)} \,dx \,dy$

Published on 16 Apr 2026 - 23:09

118

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Calculate $\int_{1}^{\infty}\frac{x\ln x}{(1+x^2)^2}\text{dx}$

Published on 17 Apr 2026 - 6:06

154

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Evaluate $\int\limits_0^{\ln{2}}\ln(1+e^x)\ln(1-e^x)dx$

Published on 16 Apr 2026 - 18:54

166

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Integrating $\int_0^1 \frac{\ln(1-x)}{1+s^2 x^2}dx$

Published on 18 Apr 2026 - 15:00

51

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Find a function under the integral sign

Published on 12 Apr 2026 - 6:58

180

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$f$ and $1/p$ are positive and decreasing, $\int_1^\infty f<\infty$, $\int_1^\infty\frac{1}{p}=\infty$, show $\lim_{x\rightarrow \infty}p(x)f(x)=0$

Published on 17 Apr 2026 - 10:25

55

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What's wrong with this solution to this improper integral?

Published on 12 Apr 2026 - 5:29

698

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Is there a continuous version of the Taylor Series?

Published on 14 Apr 2026 - 3:59

391

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Evaluating two improper integrals involving powers of $\sin(t)$

Published on 11 Apr 2026 - 22:26

173

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Show $\int_{0}^{\infty}\frac{\sin x^{2}}{\pi-x^{2}}dx=\frac{\sqrt{\pi}}{2}\left[C(\sqrt{2})+S(\sqrt{2})\right]$

Published on 17 Apr 2026 - 8:14

List Question

Show that $\int_0^e \ln(1-\ln(x))dx=-e\gamma$

Improper integral asymptote shortcut

Finiteness of the integral of the square of a non-negative continuous unbounded function

How to find the solution for this integral equation?

Help with a limit about $F(x) = \displaystyle\int_1^x \frac{ \log t}{(t+a)(t-1)} dt$

Calculate $I = \int_{0}^{\infty} \int_{0}^{\infty} \frac{\ln(xy)}{(x^2 + x + 1)(y^2 + y + 1)} \,dx \,dy$

Calculate $\int_{1}^{\infty}\frac{x\ln x}{(1+x^2)^2}\text{dx}$

Evaluate $\int\limits_0^{\ln{2}}\ln(1+e^x)\ln(1-e^x)dx$

Integrating $\int_0^1 \frac{\ln(1-x)}{1+s^2 x^2}dx$

Find a function under the integral sign

$f$ and $1/p$ are positive and decreasing, $\int_1^\infty f<\infty$, $\int_1^\infty\frac{1}{p}=\infty$, show $\lim_{x\rightarrow \infty}p(x)f(x)=0$

What's wrong with this solution to this improper integral?

Is there a continuous version of the Taylor Series?

Evaluating two improper integrals involving powers of $\sin(t)$

Show $\int_{0}^{\infty}\frac{\sin x^{2}}{\pi-x^{2}}dx=\frac{\sqrt{\pi}}{2}\left[C(\sqrt{2})+S(\sqrt{2})\right]$

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