List questions from improper-integrals

Published on 13 Apr 2026 - 23:02

30

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Asymptotic behavior of the integrand in a stochastic integral

Published on 13 Apr 2026 - 17:17

44

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$\int_0^\infty \frac{dt}{(1+t)(2+t)...(n+t)}$

Published on 17 Apr 2026 - 1:58

96

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How to evaluate $\int_{-\infty}^{\infty} \frac{\cos((b) (r) (u) (h^2))}{(h^2) (r) (u) (b)} (h) \tan^{-1}(h) \, dh$

Published on 15 Apr 2026 - 10:42

120

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Derive a closed-form expression for $\int\limits_0^\infty \frac{u \operatorname{J}_0(xu)}{\sqrt{1+u^2} \sqrt{1+\beta u^2}} \, \mathrm{d} u$

Published on 15 Apr 2026 - 19:20

113

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Infinite integral of $e^{-\alpha t^\beta} \cos(\omega t)$

Published on 15 Apr 2026 - 21:05

220

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$\int_0^\infty \frac{u}{u^2+\sigma^2} \, J_{4m} (u) \, \mathrm{d} u = K_{4m}(\sigma) + ?$

Published on 16 Apr 2026 - 6:10

90

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How to prove $\int_1^{+\infty} x^{1-a}\mathrm{d}x/\sqrt{x^2-1}$ converges when $a>1$

Published on 15 Apr 2026 - 0:19

35

Views

Prove that $\lim_{R\to 0}\int_R^\infty 2n_0 (\frac{r_0}{r})^{\alpha} \frac{r\mathrm{d}r}{\sqrt{r^2-R^2}}$ converges when $a<1$

Published on 15 Apr 2026 - 4:42

39

Views

Well posedness integral by parts

Published on 17 Apr 2026 - 5:49

131

Views

Proving $\int_0^\infty \frac{x}{(1+x)^3} dx = \frac{1}{2} \int_0^\infty \frac{1}{(1+x)^2} dx$

Published on 16 Apr 2026 - 21:05

169

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Integral of form $\int \frac{1}{ \sqrt{-a x^2 + b x + c}} dx$

Published on 16 Apr 2026 - 5:38

56

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Differentiation under integral sign - problem while finding the constant c

Published on 11 Apr 2026 - 22:23

45

Views

Calculate $\int_{0}^{+\infty} \frac{x^3}{e^x-1}dx$

Published on 15 Apr 2026 - 23:31

75

Views

Convergent integral

Published on 11 Apr 2026 - 14:19

List Question

Solving Improper Rational Trig Integral

Asymptotic behavior of the integrand in a stochastic integral

$\int_0^\infty \frac{dt}{(1+t)(2+t)...(n+t)}$

How to evaluate $\int_{-\infty}^{\infty} \frac{\cos((b) (r) (u) (h^2))}{(h^2) (r) (u) (b)} (h) \tan^{-1}(h) \, dh$

Derive a closed-form expression for $\int\limits_0^\infty \frac{u \operatorname{J}_0(xu)}{\sqrt{1+u^2} \sqrt{1+\beta u^2}} \, \mathrm{d} u$

Infinite integral of $e^{-\alpha t^\beta} \cos(\omega t)$

$\int_0^\infty \frac{u}{u^2+\sigma^2} \, J_{4m} (u) \, \mathrm{d} u = K_{4m}(\sigma) + ?$

How to prove $\int_1^{+\infty} x^{1-a}\mathrm{d}x/\sqrt{x^2-1}$ converges when $a>1$

Prove that $\lim_{R\to 0}\int_R^\infty 2n_0 (\frac{r_0}{r})^{\alpha} \frac{r\mathrm{d}r}{\sqrt{r^2-R^2}}$ converges when $a<1$

Well posedness integral by parts

Proving $\int_0^\infty \frac{x}{(1+x)^3} dx = \frac{1}{2} \int_0^\infty \frac{1}{(1+x)^2} dx$

Integral of form $\int \frac{1}{ \sqrt{-a x^2 + b x + c}} dx$

Differentiation under integral sign - problem while finding the constant c

Calculate $\int_{0}^{+\infty} \frac{x^3}{e^x-1}dx$

Convergent integral

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