Question

Can't prove the integral of two variables converges

score 28 · Answer 1 · 2026-04-11 11:16:10

28

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Can't prove the integral of two variables converges

Published on 11 Apr 2026 - 11:16

score 128 · Answer 2 · 2026-03-27 12:16:54

128

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Prove that $\int \limits_{0}^{\infty} x^p e^{-g(x)/x} dx \leq e^{p+1} \int \limits_{0}^{\infty} x^p e^{-g'(x)}dx$.

Published on 27 Mar 2026 - 12:16

score 3.2k · Answer 3 · 2026-04-06 00:35:40

3.2k

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If $0\leq f(x)\leq g(x)$, and $\int^{\infty}_{a}g(x)dx$ diverges, so does $\int_a^\infty f(x)\,dx$?

Published on 06 Apr 2026 - 0:35

score 55 · Answer 4 · 2026-04-07 23:17:10

55

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Explore the continuity $\int_{0}^{1} \arctan{\frac{x}{y}}dx$

Published on 07 Apr 2026 - 23:17

score 145 · Answer 5 · 2017-02-24 18:07:20

145

Views

Calculate using Euler integrals $\int \limits_{-1}^{1} \frac{dx}{\sqrt[3]{(1+x)^2(1-x)}}$

Published on 24 Feb 2017 - 18:07

score 300 · Answer 6 · 2017-02-25 00:40:35

300

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Why is the integral $\int_{1}^{\infty} \tan \left(1/n\right) \mathbb{d}n$ divergent on $[1,\infty)$?

Published on 25 Feb 2017 - 0:40

score 705 · Answer 7 · 2017-02-25 06:51:10

705

Views

Improper integral of natural log over a quadratic

Published on 25 Feb 2017 - 6:51

score 80 · Answer 8 · 2017-02-25 08:10:24

80

Views

Calculate using Euler integrals $\int \limits_0^{+\infty} \frac{1}{x^{n+1}} e^{-\frac{\alpha}{2x^2}}dx$

Published on 25 Feb 2017 - 8:10

score 2k · Answer 9 · 2026-04-03 09:13:51

2k

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Prove $B(p, q) = \int \limits_0^1 \frac{x^{p-1} + x^{q-1}}{(1+x)^{p+q}}dx$

Published on 03 Apr 2026 - 9:13

score 16 · Answer 10 · 2026-03-10 10:06:07

Is it possible to know that $\frac{\partial}{\partial y} \int_{-\infty}^{g(y)} f(x) dx = (g(y))\cdot \frac{\partial}{\partial y}g(y)$?

score 102 · Answer 11 · 2026-04-11 20:02:08

102

Views

Unsure why this improper integral converges at 2.

Published on 11 Apr 2026 - 20:02

score 43 · Answer 12 · 2026-04-12 14:05:57

43

Views

A divergence removed (or not) from an integral.

Published on 12 Apr 2026 - 14:05

score 217 · Answer 13 · 2017-02-26 18:52:38

217

Views

Prove uniform convergence $\int \limits_2^{+\infty} \frac{1}{x\ln(x)^{\alpha}}dx$

Published on 26 Feb 2017 - 18:52

score 39 · Answer 14 · 2026-04-11 20:58:50

39

Views

Convergence of improper integral: finding $p \in \mathbb{R}$

Published on 11 Apr 2026 - 20:58

score 271 · Answer 15 · 2026-03-30 03:54:49

271

Views

Different ways to evaluate $\int_0^\infty xI_0(2x)e^{-x^2}\,dx$

Published on 30 Mar 2026 - 3:54

List Question

Can't prove the integral of two variables converges

Prove that $\int \limits_{0}^{\infty} x^p e^{-g(x)/x} dx \leq e^{p+1} \int \limits_{0}^{\infty} x^p e^{-g'(x)}dx$.

If $0\leq f(x)\leq g(x)$, and $\int^{\infty}_{a}g(x)dx$ diverges, so does $\int_a^\infty f(x)\,dx$?

Explore the continuity $\int_{0}^{1} \arctan{\frac{x}{y}}dx$

Calculate using Euler integrals $\int \limits_{-1}^{1} \frac{dx}{\sqrt[3]{(1+x)^2(1-x)}}$

Why is the integral $\int_{1}^{\infty} \tan \left(1/n\right) \mathbb{d}n$ divergent on $[1,\infty)$?

Improper integral of natural log over a quadratic

Calculate using Euler integrals $\int \limits_0^{+\infty} \frac{1}{x^{n+1}} e^{-\frac{\alpha}{2x^2}}dx$

Prove $B(p, q) = \int \limits_0^1 \frac{x^{p-1} + x^{q-1}}{(1+x)^{p+q}}dx$

Is it possible to know that $\frac{\partial}{\partial y} \int_{-\infty}^{g(y)} f(x) dx = (g(y))\cdot \frac{\partial}{\partial y}g(y)$?

Unsure why this improper integral converges at 2.

A divergence removed (or not) from an integral.

Prove uniform convergence $\int \limits_2^{+\infty} \frac{1}{x\ln(x)^{\alpha}}dx$

Convergence of improper integral: finding $p \in \mathbb{R}$

Different ways to evaluate $\int_0^\infty xI_0(2x)e^{-x^2}\,dx$

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