Question

How to evaluate $\int_{0}^{\infty} x^4 e^{-0.5x^2} dx$

score 114 · Answer 1 · 2026-04-14 22:15:41

114

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How to evaluate $\int_{0}^{\infty} x^4 e^{-0.5x^2} dx$

Published on 14 Apr 2026 - 22:15

score 48 · Answer 2 · 2026-04-14 22:29:41

48

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Behavior of a function in $H^1_0(\mathbb{R})$ at the origin

Published on 14 Apr 2026 - 22:29

score 111 · Answer 3 · 2026-04-16 06:41:51

111

Views

Does the double integral diverge? $\iint_{\Omega} \sqrt{\frac{x^2 + y^2}{xy(1 - x^2 - y^2)}} ~ dx dy$

Published on 16 Apr 2026 - 6:41

score 388 · Answer 4 · 2026-04-16 20:29:03

388

Views

Integrating $\int_0^\infty\frac{u^2}{\sqrt{u^2+a^2}}J_1(ru)e^{-z\sqrt{u^2+a^2}}du$

Published on 16 Apr 2026 - 20:29

score 143 · Answer 5 · 2026-04-16 12:02:46

143

Views

Prove that $\int_{0}^{+\infty}f(x) dx < +\infty$ then $\displaystyle \lim_{x \to +\infty}xf(x) =0$.

Published on 16 Apr 2026 - 12:02

score 147 · Answer 6 · 2026-04-16 14:11:00

147

Views

Evaluate $\int_0^1 dx \phantom{1} (1-x)^{\alpha} x^{\beta} \left( (1-x)^2 a + x^2 b \right)^{-\frac{\alpha+\beta}{2}}$ in terms of Gamma functions

Published on 16 Apr 2026 - 14:11

score 39 · Answer 7 · 2026-04-10 15:22:51

39

Views

How to evaluate 2D inverse Fourier transform?

Published on 10 Apr 2026 - 15:22

score 107 · Answer 8 · 2026-04-16 22:45:21

107

Views

Evaluate $ \int\limits_0^{+\infty} x \tanh^{-1}\left(\frac{k x}{a}\right) \exp\left(-\frac{x^2}{b}\right) dx $

Published on 16 Apr 2026 - 22:45

score 126 · Answer 9 · 2026-04-16 04:48:18

126

Views

Compute residues for $\int_{-\infty}^{\infty} \frac{x \sin x}{1+x^4}dx$

Published on 16 Apr 2026 - 4:48

score 86 · Answer 10 · 2026-04-16 23:22:21

86

Views

Evaluate: $\int_{0}^{\infty} x^{a} (1+x)^{b} dx$

Published on 16 Apr 2026 - 23:22

score 43 · Answer 11 · 2026-04-15 13:05:02

43

Views

Feynman parametrization for $\frac{1}{\prod_{i=1}^N A_i^{\lambda_i}}$

Published on 15 Apr 2026 - 13:05

score 110 · Answer 12 · 2026-04-14 08:30:00

110

Views

How might one prove the following is either possible or impossible?

Published on 14 Apr 2026 - 8:30

score 81 · Answer 13 · 2026-04-13 17:41:24

81

Views

Riemann integral-Real analysis-infinity cases

Published on 13 Apr 2026 - 17:41

score 49 · Answer 14 · 2026-04-11 17:27:58

49

Views

Does absolute convergence of an integal imply that it is equal to the limit of the integral on $[-c,c]$ as $c\to \infty$?

Published on 11 Apr 2026 - 17:27

score 117 · Answer 15 · 2026-04-17 07:10:16

117

Views

Where is the contradiction? $I=\int_0^\infty \frac{a^x}{x^2+1}dx,~~0<a<1$

Published on 17 Apr 2026 - 7:10

List Question

How to evaluate $\int_{0}^{\infty} x^4 e^{-0.5x^2} dx$

Behavior of a function in $H^1_0(\mathbb{R})$ at the origin

Does the double integral diverge? $\iint_{\Omega} \sqrt{\frac{x^2 + y^2}{xy(1 - x^2 - y^2)}} ~ dx dy$

Integrating $\int_0^\infty\frac{u^2}{\sqrt{u^2+a^2}}J_1(ru)e^{-z\sqrt{u^2+a^2}}du$

Prove that $\int_{0}^{+\infty}f(x) dx < +\infty$ then $\displaystyle \lim_{x \to +\infty}xf(x) =0$.

Evaluate $\int_0^1 dx \phantom{1} (1-x)^{\alpha} x^{\beta} \left( (1-x)^2 a + x^2 b \right)^{-\frac{\alpha+\beta}{2}}$ in terms of Gamma functions

How to evaluate 2D inverse Fourier transform?

Evaluate $ \int\limits_0^{+\infty} x \tanh^{-1}\left(\frac{k x}{a}\right) \exp\left(-\frac{x^2}{b}\right) dx $

Compute residues for $\int_{-\infty}^{\infty} \frac{x \sin x}{1+x^4}dx$

Evaluate: $\int_{0}^{\infty} x^{a} (1+x)^{b} dx$

Feynman parametrization for $\frac{1}{\prod_{i=1}^N A_i^{\lambda_i}}$

How might one prove the following is either possible or impossible?

Riemann integral-Real analysis-infinity cases

Does absolute convergence of an integal imply that it is equal to the limit of the integral on $[-c,c]$ as $c\to \infty$?

Where is the contradiction? $I=\int_0^\infty \frac{a^x}{x^2+1}dx,~~0<a<1$

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