Question

Proof $\Re{\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{1}{\tan^{2n}(x)+1}dx}=\frac{\pi}{2},\forall n \in \mathbb{R}$

score 110 · Answer 1 · 2018-07-30 22:42:13

110

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Proof $\Re{\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{1}{\tan^{2n}(x)+1}dx}=\frac{\pi}{2},\forall n \in \mathbb{R}$

Published on 30 Jul 2018 - 22:42

score 182 · Answer 2 · 2018-07-31 05:38:24

182

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Convergence of integral in complex analysis textbook

Published on 31 Jul 2018 - 5:38

score 74 · Answer 3 · 2018-07-31 19:24:20

74

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What do improper integrals represent?

Published on 31 Jul 2018 - 19:24

score 91 · Answer 4 · 2018-07-31 22:28:48

91

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A continuous function $f$ verifies : $\int_{0}^{+\infty} f(x).dx= +\infty$. $\int_{-\infty}^{0} f(x).dx= -\infty$.

Published on 31 Jul 2018 - 22:28

score 67 · Answer 5 · 2018-08-01 07:05:19

67

Views

Determine convergence of an improper integral

Published on 01 Aug 2018 - 7:05

score 705 · Answer 6 · 2018-08-02 19:19:09

705

Views

Prove that $\int_0^\infty\,\frac{\sin(kx)}{x(x^2+1)}\,\text{d}x=\frac{\pi}{2}\,\left(1-\exp(-k)\right)$ for all $k\in\mathbb{R}_{\ge0}$.

Published on 02 Aug 2018 - 19:19

score 202 · Answer 7 · 2018-08-04 18:30:49

202

Views

Determine whether this improper integral converges or not

Published on 04 Aug 2018 - 18:30

score 94 · Answer 8 · 2018-08-05 11:22:01

94

Views

Evaluation of an Improper Integral on $\mathbb{R^2}$

Published on 05 Aug 2018 - 11:22

score 140 · Answer 9 · 2018-08-05 11:52:23

140

Views

Is my solution for this integral problem correct?

Published on 05 Aug 2018 - 11:52

score 1.2k · Answer 10 · 2018-08-05 14:45:49

1.2k

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Determine whether the integral $ \int^{+\infty}_0\frac{e^{-t}} {\sqrt t} \, dt$ converges or diverges?

Published on 05 Aug 2018 - 14:45

score 134 · Answer 11 · 2018-08-07 04:47:04

134

Views

How to compute $ \frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty \frac{e^{-{x^2}/{2}}}{1+e^{-(ax+b)}}\,\mathrm dx $ when $b \ne 0$

Published on 07 Aug 2018 - 4:47

score 34 · Answer 12 · 2018-08-07 18:35:15

34

Views

Finiteness of improper integral given limit of function

Published on 07 Aug 2018 - 18:35

score 293 · Answer 13 · 2026-03-25 06:01:45

293

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Improper/extended multiple integral and change of variables

Published on 25 Mar 2026 - 6:01

score 494 · Answer 14 · 2018-08-08 16:11:27

494

Views

Show that $\lim_{x \to \infty} \int_0 ^x \cos (t^3 + t) \,dt$ exists

Published on 08 Aug 2018 - 16:11

score 367 · Answer 15 · 2018-08-08 16:40:14

367

Views

How to prove that $\int_{-\infty}^{\infty}f'(t)\exp(-t^2)\text{d}t$ is finite when $\lim_{|t|\to \infty}f(t)\exp(-t^2) = 0$?

Published on 08 Aug 2018 - 16:40

List Question

Proof $\Re{\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{1}{\tan^{2n}(x)+1}dx}=\frac{\pi}{2},\forall n \in \mathbb{R}$

Convergence of integral in complex analysis textbook

What do improper integrals represent?

A continuous function $f$ verifies : $\int_{0}^{+\infty} f(x).dx= +\infty$. $\int_{-\infty}^{0} f(x).dx= -\infty$.

Determine convergence of an improper integral

Prove that $\int_0^\infty\,\frac{\sin(kx)}{x(x^2+1)}\,\text{d}x=\frac{\pi}{2}\,\left(1-\exp(-k)\right)$ for all $k\in\mathbb{R}_{\ge0}$.

Determine whether this improper integral converges or not

Evaluation of an Improper Integral on $\mathbb{R^2}$

Is my solution for this integral problem correct?

Determine whether the integral $ \int^{+\infty}_0\frac{e^{-t}} {\sqrt t} \, dt$ converges or diverges?

How to compute $ \frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty \frac{e^{-{x^2}/{2}}}{1+e^{-(ax+b)}}\,\mathrm dx $ when $b \ne 0$

Finiteness of improper integral given limit of function

Improper/extended multiple integral and change of variables

Show that $\lim_{x \to \infty} \int_0 ^x \cos (t^3 + t) \,dt$ exists

How to prove that $\int_{-\infty}^{\infty}f'(t)\exp(-t^2)\text{d}t$ is finite when $\lim_{|t|\to \infty}f(t)\exp(-t^2) = 0$?

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