List questions from improper-integrals

Published on 14 Apr 2026 - 5:16

132

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Convergence of $\int_0^\infty \frac{\sqrt{x}\sin x}{(e^x-1)\log(1+x)}dx$

Published on 16 Apr 2026 - 4:53

194

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finding the free energy of a van der waals gas (integration)

Published on 09 Apr 2026 - 23:19

122

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Relation between Nuttal Q-function and Gaussian Q-function

Published on 15 Apr 2026 - 12:53

623

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Proving the transform of the Q-function

Published on 14 Apr 2026 - 15:33

109

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Convergence of improper integral $\int_0^1 \frac{x^\alpha}{x+x^2}dx$ for $\alpha>0$

Published on 15 Apr 2026 - 19:13

638

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Proof of certain Gaussian integral form

Published on 12 Apr 2026 - 6:44

119

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Question on Newman's proof of the Prime Number Theorem

Published on 13 Apr 2026 - 5:21

275

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Various evalutions of $\int_0^\infty \sin x \sin \sqrt{x} \,dx$

Published on 15 Apr 2026 - 6:51

2k

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Determine whether it is convergent or divergent: $\int_{-1}^0 {\frac{e^{1/x}}{x^3}}dx$

Published on 17 Apr 2026 - 5:22

77

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Integration of this using a multi-dimensional hypergeometric function

Published on 26 Mar 2026 - 9:44

2.8k

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How to solve a hard integral?

Published on 11 Apr 2026 - 11:46

149

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Evaluating the improper integral $\int_0^1 \frac{\log (x \sqrt{x})}{\sqrt{x}} \,dx$

Published on 16 Apr 2026 - 2:01

541

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Show that $\int_1^{\infty } \frac{(\ln x)^2}{x^2+x+1} \, dx = \frac{8 \pi ^3}{81 \sqrt{3}}$

Published on 16 Apr 2026 - 19:01

702

Views

Prove that $f(a)=f(b)$ if $\int_{-\infty}^{\infty}f(x)dx=1$

Published on 15 Apr 2026 - 21:06

List Question

Improper and definitive integral of trigonometric functions involving absolute values

Convergence of $\int_0^\infty \frac{\sqrt{x}\sin x}{(e^x-1)\log(1+x)}dx$

finding the free energy of a van der waals gas (integration)

Relation between Nuttal Q-function and Gaussian Q-function

Proving the transform of the Q-function

Convergence of improper integral $\int_0^1 \frac{x^\alpha}{x+x^2}dx$ for $\alpha>0$

Proof of certain Gaussian integral form

Question on Newman's proof of the Prime Number Theorem

Various evalutions of $\int_0^\infty \sin x \sin \sqrt{x} \,dx$

Determine whether it is convergent or divergent: $\int_{-1}^0 {\frac{e^{1/x}}{x^3}}dx$

Integration of this using a multi-dimensional hypergeometric function

How to solve a hard integral?

Evaluating the improper integral $\int_0^1 \frac{\log (x \sqrt{x})}{\sqrt{x}} \,dx$

Show that $\int_1^{\infty } \frac{(\ln x)^2}{x^2+x+1} \, dx = \frac{8 \pi ^3}{81 \sqrt{3}}$

Prove that $f(a)=f(b)$ if $\int_{-\infty}^{\infty}f(x)dx=1$

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