Question

How to show $\ \int_1^\infty\frac1xdx\ $ diverges (not using the harmonic series)?

score 1.3k · Answer 1 · 2026-04-11 18:44:20

1.3k

Views

How to show $\ \int_1^\infty\frac1xdx\ $ diverges (not using the harmonic series)?

Published on 11 Apr 2026 - 18:44

score 115 · Answer 2 · 2026-04-16 07:47:44

115

Views

what is the integral $\int_{0}^1 \sqrt{(1+(1/x^2))}dx$

Published on 16 Apr 2026 - 7:47

score 97 · Answer 3 · 2026-04-09 21:36:55

97

Views

How can I resolve this improper integral?

Published on 09 Apr 2026 - 21:36

score 270 · Answer 4 · 2026-04-16 19:40:12

270

Views

A difficult integral $\int_0^{\infty} \frac{\sin 2t}{1+t^3}\, {\rm d}t$

Published on 16 Apr 2026 - 19:40

score 338 · Answer 5 · 2026-04-17 03:37:58

338

Views

Computing $\lim_{\epsilon \rightarrow 0} \int_0^\infty \frac{\sin x}{x} \arctan{\frac{x}{\epsilon}}dx$

Published on 17 Apr 2026 - 3:37

score 223 · Answer 6 · 2026-04-14 19:29:57

223

Views

Integrating $\frac{\sec^2\theta}{1+\tan^2\theta \cos^2(2\alpha)}$ with respect to $\theta$

Published on 14 Apr 2026 - 19:29

score 410 · Answer 7 · 2026-04-11 21:32:02

410

Views

Integral of reciprocal absolute value function

Published on 11 Apr 2026 - 21:32

score 314 · Answer 8 · 2026-04-13 15:20:18

314

Views

Help with a limit of an integral: $\lim_{h\to \infty}h\int_{0}^\infty{{ {e}^{-hx}f(x)} dx}=f(0)$

Published on 13 Apr 2026 - 15:20

score 176 · Answer 9 · 2026-04-14 20:53:27

176

Views

Exchanging the order of integration in $ \int_0^\infty \int_{-\infty}^\infty \sin(x^2)x e^{-t^2 x^2} dt dx$?

Published on 14 Apr 2026 - 20:53

score 100 · Answer 10 · 2026-04-16 09:18:04

100

Views

What is wrong with my method of computing $\int_0^{\infty}x^2 e^{-x^2} \space dx$

Published on 16 Apr 2026 - 9:18

score 68 · Answer 11 · 2026-04-14 11:11:04

68

Views

Finding the value of an integral containing $(\ln x)^2$ in the denominator

Published on 14 Apr 2026 - 11:11

score 64 · Answer 12 · 2026-04-16 12:14:18

64

Views

Integrate $\int_{-\infty}^{+\infty} \frac{1}{\sqrt{P(x)}}e^{-ax^2 - bx - c}dx$ where $P$ is a polynomial of degree $6$

Published on 16 Apr 2026 - 12:14

score 183 · Answer 13 · 2026-04-16 12:21:29

183

Views

Is there a direct method for evaluating this integral: $\int_{0}^{2\pi}\ln^2(2\sin(\frac{x}{2}))dx$?

Published on 16 Apr 2026 - 12:21

score 94 · Answer 14 · 2026-04-15 16:12:13

94

Views

$0<\int_0^\infty\frac{\sin t}{\ln(1+x+t)} dt<\frac{2}{\ln(1+x)}$

Published on 15 Apr 2026 - 16:12

score 326 · Answer 15 · 2026-04-15 18:35:30

326

Views

How to calculate: $ \lim \limits_{x \to 0^+} \frac{\int_{0}^{x} (e^{t^2}-1)dt}{{\int_{0}^{x^2} \sin(t)dt}} $

Published on 15 Apr 2026 - 18:35

List Question

How to show $\ \int_1^\infty\frac1xdx\ $ diverges (not using the harmonic series)?

what is the integral $\int_{0}^1 \sqrt{(1+(1/x^2))}dx$

How can I resolve this improper integral?

A difficult integral $\int_0^{\infty} \frac{\sin 2t}{1+t^3}\, {\rm d}t$

Computing $\lim_{\epsilon \rightarrow 0} \int_0^\infty \frac{\sin x}{x} \arctan{\frac{x}{\epsilon}}dx$

Integrating $\frac{\sec^2\theta}{1+\tan^2\theta \cos^2(2\alpha)}$ with respect to $\theta$

Integral of reciprocal absolute value function

Help with a limit of an integral: $\lim_{h\to \infty}h\int_{0}^\infty{{ {e}^{-hx}f(x)} dx}=f(0)$

Exchanging the order of integration in $ \int_0^\infty \int_{-\infty}^\infty \sin(x^2)x e^{-t^2 x^2} dt dx$?

What is wrong with my method of computing $\int_0^{\infty}x^2 e^{-x^2} \space dx$

Finding the value of an integral containing $(\ln x)^2$ in the denominator

Integrate $\int_{-\infty}^{+\infty} \frac{1}{\sqrt{P(x)}}e^{-ax^2 - bx - c}dx$ where $P$ is a polynomial of degree $6$

Is there a direct method for evaluating this integral: $\int_{0}^{2\pi}\ln^2(2\sin(\frac{x}{2}))dx$?

$0<\int_0^\infty\frac{\sin t}{\ln(1+x+t)} dt<\frac{2}{\ln(1+x)}$

How to calculate: $ \lim \limits_{x \to 0^+} \frac{\int_{0}^{x} (e^{t^2}-1)dt}{{\int_{0}^{x^2} \sin(t)dt}} $

Trending Questions

Popular # Hahtags

Popular Questions