List questions from improper-integrals

Published on 08 Apr 2026 - 1:37

100

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How to prove $\int_0^\infty\int_0^\infty e^{-x^2 -y^2}dxdy= (\int_0^\infty e^{-x^2}dx)(\int_0^\infty e^{-y^2}dy)$?

Published on 10 Jun 2020 - 20:47

65

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How to prove $ \int_{1}^{ \infty} \frac{1}{ (1+x^3)^3 } dx$ is convergent?

Published on 11 Jun 2020 - 8:17

727

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Improper integrals where both limits are infinite

Published on 11 Jun 2020 - 11:58

22

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Convergence of the integral(help with my appeal).

Published on 11 Jun 2020 - 13:10

98

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How to evaluate this factorial-related integral?

Published on 28 Mar 2026 - 10:03

51

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Evaluate: $\int_{0}^{\pi} \frac{\cos x \cos{(A \cos x)}}{B \cos x +C \sin x}\,dx$

Published on 12 Jun 2020 - 13:46

179

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Convergence of hankel transform for polynomials

Published on 25 Mar 2026 - 12:55

91

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For which $\alpha$ the integral converges $\iint_{\mathbb{R}^2}\frac{dx\,dy}{(x^2-xy+y^2+1)^\alpha}$?

Published on 13 Jun 2020 - 6:04

124

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Using residue theorem to calculate $\int\limits_{-\infty}^{\infty} \frac{\cos(2x)\,dx}{(x^2+2x+2)^2}$

Published on 30 Mar 2026 - 15:14

368

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Integral $\int_0^{\infty} \frac{\sin^3{x}}{x} \; dx$

Published on 13 Jun 2020 - 17:35

83

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Convergence test for an integral of bounds $0$ to $1$

Published on 14 Jun 2020 - 0:19

67

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Convergence of $\int_0^1 x^p \ln^q \left(\frac{1}{x}\right)dx$ without using Gamma function

Published on 14 Jun 2020 - 12:03

28

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Exact equations & integrating factors

Published on 14 Jun 2020 - 14:32

255

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How do you prove that $\int_0^\infty \frac{\sin(2x)}{1-e^{2\pi x}} dx = \frac{1}{2-2e^2}$?

Published on 14 Jun 2020 - 16:28

List Question

Evaluating improper definite integrals

How to prove $\int_0^\infty\int_0^\infty e^{-x^2 -y^2}dxdy= (\int_0^\infty e^{-x^2}dx)(\int_0^\infty e^{-y^2}dy)$?

How to prove $ \int_{1}^{ \infty} \frac{1}{ (1+x^3)^3 } dx$ is convergent?

Improper integrals where both limits are infinite

Convergence of the integral(help with my appeal).

How to evaluate this factorial-related integral?

Evaluate: $\int_{0}^{\pi} \frac{\cos x \cos{(A \cos x)}}{B \cos x +C \sin x}\,dx$

Convergence of hankel transform for polynomials

For which $\alpha$ the integral converges $\iint_{\mathbb{R}^2}\frac{dx\,dy}{(x^2-xy+y^2+1)^\alpha}$?

Using residue theorem to calculate $\int\limits_{-\infty}^{\infty} \frac{\cos(2x)\,dx}{(x^2+2x+2)^2}$

Integral $\int_0^{\infty} \frac{\sin^3{x}}{x} \; dx$

Convergence test for an integral of bounds $0$ to $1$

Convergence of $\int_0^1 x^p \ln^q \left(\frac{1}{x}\right)dx$ without using Gamma function

Exact equations & integrating factors

How do you prove that $\int_0^\infty \frac{\sin(2x)}{1-e^{2\pi x}} dx = \frac{1}{2-2e^2}$?

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