Question

Solving $\int_0^{\infty} \sin(ax^2)\sin(b/x^2)\,\mathrm dx$

score 492 · Answer 1 · 2026-04-16 12:57:30

492

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Solving $\int_0^{\infty} \sin(ax^2)\sin(b/x^2)\,\mathrm dx$

Published on 16 Apr 2026 - 12:57

score 140 · Answer 2 · 2026-04-17 11:47:24

140

Views

Not able to solve $\int\limits_1^n \frac{g(x)}{x^{p+1}} \mathrm dx $

Published on 17 Apr 2026 - 11:47

score 278 · Answer 3 · 2026-04-17 12:35:31

Test for convergence of improper integrals $\int_{0}^{1}\frac{\sqrt{x}}{(1+x)\ln^3(1+x)}dx$ and $\int_{1}^{\infty}\frac{\sqrt{x}}{(1+x)\ln^3(1+x)}dx$

score 1.3k · Answer 4 · 2026-04-16 04:15:49

1.3k

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Evaluate the integral $\int_{0}^{\infty} \frac{1}{(1+x^2)\cosh{(ax)}}dx$

Published on 16 Apr 2026 - 4:15

score 99 · Answer 5 · 2026-04-11 16:58:32

99

Views

Problem in computing of integral by substitution.

Published on 11 Apr 2026 - 16:58

score 379 · Answer 6 · 2026-04-16 19:40:12

379

Views

A difficult integral $\int_0^\infty \mathrm{d}t\frac{1}{t}\frac{1}{t-s-\mathrm{i}\epsilon}\frac{1}{X}\ln\frac{1-X}{1+X} $

Published on 16 Apr 2026 - 19:40

score 284 · Answer 7 · 2026-04-12 23:06:12

284

Views

How can I evaluate $\int_0^\infty \frac{\sin x}{x} \,dx$? [may be duplicated]

Published on 12 Apr 2026 - 23:06

score 1.4k · Answer 8 · 2026-04-14 05:04:06

1.4k

Views

How can I calculate $\int_0^\infty \frac{u^3}{(e^u-1)} \, du$?

Published on 14 Apr 2026 - 5:04

score 8.2k · Answer 9 · 2026-04-13 23:24:23

8.2k

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Proving Abel-Dirichlet's test for convergence of improper integrals using Integration by parts

Published on 13 Apr 2026 - 23:24

score 1.8k · Answer 10 · 2026-04-11 13:14:53

1.8k

Views

A convergence test for improper integrals ($\mu$-test)

Published on 11 Apr 2026 - 13:14

score 852 · Answer 11 · 2026-04-15 03:00:22

852

Views

does $\intop_{1}^{\infty}x\sin(x^{3})dx$ really converge?

Published on 15 Apr 2026 - 3:00

score 380 · Answer 12 · 2026-04-15 12:03:06

380

Views

How to find $\int_0^{2\pi} \frac{dt}{1+2\cos(t)}$

Published on 15 Apr 2026 - 12:03

score 2.9k · Answer 13 · 2026-04-16 16:15:38

2.9k

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Evaluate $\int_0^\infty \frac{\log(1+x^3)}{(1+x^2)^2}dx$ and $\int_0^\infty \frac{\log(1+x^4)}{(1+x^2)^2}dx$

Published on 16 Apr 2026 - 16:15

score 888 · Answer 14 · 2026-04-16 22:47:13

888

Views

Evaluting $\int_{1}^{2} \frac{\tan^{-1} x}{\tan^{-1} \frac {1}{x^2-3x+3}} \operatorname dx$

Published on 16 Apr 2026 - 22:47

score 45 · Answer 15 · 2026-04-10 18:36:40

45

Views

Cauchy principal value and the "normal" definition.

Published on 10 Apr 2026 - 18:36

List Question

Solving $\int_0^{\infty} \sin(ax^2)\sin(b/x^2)\,\mathrm dx$

Not able to solve $\int\limits_1^n \frac{g(x)}{x^{p+1}} \mathrm dx $

Test for convergence of improper integrals $\int_{0}^{1}\frac{\sqrt{x}}{(1+x)\ln^3(1+x)}dx$ and $\int_{1}^{\infty}\frac{\sqrt{x}}{(1+x)\ln^3(1+x)}dx$

Evaluate the integral $\int_{0}^{\infty} \frac{1}{(1+x^2)\cosh{(ax)}}dx$

Problem in computing of integral by substitution.

A difficult integral $\int_0^\infty \mathrm{d}t\frac{1}{t}\frac{1}{t-s-\mathrm{i}\epsilon}\frac{1}{X}\ln\frac{1-X}{1+X} $

How can I evaluate $\int_0^\infty \frac{\sin x}{x} \,dx$? [may be duplicated]

How can I calculate $\int_0^\infty \frac{u^3}{(e^u-1)} \, du$?

Proving Abel-Dirichlet's test for convergence of improper integrals using Integration by parts

A convergence test for improper integrals ($\mu$-test)

does $\intop_{1}^{\infty}x\sin(x^{3})dx$ really converge?

How to find $\int_0^{2\pi} \frac{dt}{1+2\cos(t)}$

Evaluate $\int_0^\infty \frac{\log(1+x^3)}{(1+x^2)^2}dx$ and $\int_0^\infty \frac{\log(1+x^4)}{(1+x^2)^2}dx$

Evaluting $\int_{1}^{2} \frac{\tan^{-1} x}{\tan^{-1} \frac {1}{x^2-3x+3}} \operatorname dx$

Cauchy principal value and the "normal" definition.

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