Question

Convergence of the integral $\int_0^\infty f(x)\frac{xf'(x/(1-1/N))}{f(x/(1-1/N))}\ \mathsf dx$ as $N\to\infty$

score 124 · Answer 1 · 2026-04-16 06:27:01

124

Views

Convergence of the integral $\int_0^\infty f(x)\frac{xf'(x/(1-1/N))}{f(x/(1-1/N))}\ \mathsf dx$ as $N\to\infty$

Published on 16 Apr 2026 - 6:27

score 1.9k · Answer 2 · 2026-04-17 15:39:44

1.9k

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Improper integral complex analysis $\int_{-\infty}^\infty \frac{e^{ax} \, dx}{\cosh(x)}$

Published on 17 Apr 2026 - 15:39

score 826 · Answer 3 · 2026-04-17 13:44:43

826

Views

Prove that $\int_{0}^{\infty}{1\over x^4+x^2+1}dx=\int_{0}^{\infty}{1\over x^8+x^4+1}dx$

Published on 17 Apr 2026 - 13:44

score 220 · Answer 4 · 2026-04-16 07:47:47

220

Views

For what values of $a$ does $\int_0^\infty\left(\frac{x^a}{1 + x^2}\right)^4 \, dx$ converge?

Published on 16 Apr 2026 - 7:47

score 83 · Answer 5 · 2026-04-10 13:50:20

83

Views

Convergence of an integral involving tan function

Published on 10 Apr 2026 - 13:50

score 140 · Answer 6 · 2026-04-14 00:37:04

140

Views

proving integral equality using substitution

Published on 14 Apr 2026 - 0:37

score 132 · Answer 7 · 2026-04-17 12:38:09

132

Views

Trying to solve improper integral

Published on 17 Apr 2026 - 12:38

score 157 · Answer 8 · 2026-03-30 00:00:00

157

Views

Closed form and limit of the integral of a rational function

Published on 30 Mar 2026 - 0:00

score 95 · Answer 9 · 2026-04-16 09:39:11

95

Views

evaluate if integral converge & determine antiderivative

Published on 16 Apr 2026 - 9:39

score 232 · Answer 10 · 2026-04-17 12:18:35

232

Views

Evaluate improper integral: Exponent of square root.

Published on 17 Apr 2026 - 12:18

score 1.4k · Answer 11 · 2026-03-28 10:24:15

1.4k

Views

Integral of Fractional Part $\int_{0}^{1} \{ \frac{1}{x} \}dx$

Published on 28 Mar 2026 - 10:24

score 95 · Answer 12 · 2026-04-15 23:30:22

95

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$\int_{- \infty}^{+ \infty} |f(t)| dt < \infty \implies \int_{-\infty}^{x} f(t) dt$ is continuous?

Published on 15 Apr 2026 - 23:30

score 174 · Answer 13 · 2026-04-16 21:37:23

174

Views

If $\int_2^\infty f(x)^2 dx $ is convergent, is it true that $\int_2^\infty f(x)x^{-3/4} dx $ is convergent?

Published on 16 Apr 2026 - 21:37

score 48 · Answer 14 · 2026-04-15 14:07:37

48

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for $f\in C^2(\mathbb{R})$, finding the derivative of $\frac{d}{dt}\int_0^\infty f(x+t)\cdot xdx$

Published on 15 Apr 2026 - 14:07

score 114 · Answer 15 · 2026-04-11 13:55:00

114

Views

How much can the integrability at zero tell about the decay rate around zero?

Published on 11 Apr 2026 - 13:55

List Question

Convergence of the integral $\int_0^\infty f(x)\frac{xf'(x/(1-1/N))}{f(x/(1-1/N))}\ \mathsf dx$ as $N\to\infty$

Improper integral complex analysis $\int_{-\infty}^\infty \frac{e^{ax} \, dx}{\cosh(x)}$

Prove that $\int_{0}^{\infty}{1\over x^4+x^2+1}dx=\int_{0}^{\infty}{1\over x^8+x^4+1}dx$

For what values of $a$ does $\int_0^\infty\left(\frac{x^a}{1 + x^2}\right)^4 \, dx$ converge?

Convergence of an integral involving tan function

proving integral equality using substitution

Trying to solve improper integral

Closed form and limit of the integral of a rational function

evaluate if integral converge & determine antiderivative

Evaluate improper integral: Exponent of square root.

Integral of Fractional Part $\int_{0}^{1} \{ \frac{1}{x} \}dx$

$\int_{- \infty}^{+ \infty} |f(t)| dt < \infty \implies \int_{-\infty}^{x} f(t) dt$ is continuous?

If $\int_2^\infty f(x)^2 dx $ is convergent, is it true that $\int_2^\infty f(x)x^{-3/4} dx $ is convergent?

for $f\in C^2(\mathbb{R})$, finding the derivative of $\frac{d}{dt}\int_0^\infty f(x+t)\cdot xdx$

How much can the integrability at zero tell about the decay rate around zero?

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