Question

How do you evaluate an exponential term that contains both $-\infty$ and $+\infty$?

score 39 · Answer 1 · 2014-11-10 04:50:17

39

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How do you evaluate an exponential term that contains both $-\infty$ and $+\infty$?

Published on 10 Nov 2014 - 4:50

score 6.3k · Answer 2 · 2014-11-10 18:35:13

6.3k

Views

A strange integral: $\int_{-\infty}^{+\infty} {dx \over 1 + \left(x + \tan x\right)^2} = \pi.$

Published on 10 Nov 2014 - 18:35

score 197 · Answer 3 · 2014-11-11 04:27:27

197

Views

How to evaluate this improper integral?

Published on 11 Nov 2014 - 4:27

score 2.3k · Answer 4 · 2014-11-11 06:44:38

2.3k

Views

Does $\sum \frac{(n+4^n)}{n+6^n}$ converge or diverge?

Published on 11 Nov 2014 - 6:44

score 2.6k · Answer 5 · 2014-11-11 16:57:49

2.6k

Views

Closed form of $\int_{0}^{\infty} \frac{\tanh(x)\,\tanh(2x)}{x^2}\;dx$

Published on 11 Nov 2014 - 16:57

score 55 · Answer 6 · 2014-11-11 17:06:58

55

Views

Integral of $\int_0^{\infty} x^{4n+3} e^{-x} \sin x dx$.

Published on 11 Nov 2014 - 17:06

score 4.5k · Answer 7 · 2014-11-11 19:48:28

4.5k

Views

Determine how large the number a has to be?

Published on 11 Nov 2014 - 19:48

score 138 · Answer 8 · 2014-11-12 17:43:06

138

Views

Evaluating a specific definite integral

Published on 12 Nov 2014 - 17:43

score 172 · Answer 9 · 2026-03-25 07:39:50

172

Views

Can this divergent integral transform be regularized?

Published on 25 Mar 2026 - 7:39

score 745 · Answer 10 · 2014-11-13 00:48:46

745

Views

show $\int^\infty_0 e^{-sx} x^{-1} \sin{x} dx = \frac14 \log{(1+4s^{-2})}$ for $s>0$

Published on 13 Nov 2014 - 0:48

score 236 · Answer 11 · 2014-11-13 00:53:17

236

Views

Divergence of double integral $\iint_{x^2 + y^2 \leq 1} \frac{\mathop{d}x\mathop{d}y}{(x^2 + xy + y^2)^p},\quad p \geq 1$

Published on 13 Nov 2014 - 0:53

score 1.8k · Answer 12 · 2026-04-02 05:34:04

1.8k

Views

Orthogonality of Hermite functions

Published on 02 Apr 2026 - 5:34

score 2.7k · Answer 13 · 2014-11-13 17:18:11

2.7k

Views

Convergence of $ \int_2^\infty \frac{1}{x^q(\ln x)^p} dx $

Published on 13 Nov 2014 - 17:18

score 125 · Answer 14 · 2014-11-14 04:49:43

125

Views

Is $\int_0^{\pi/2} \sin^a(\theta)\tan(\theta) d\theta $ convergent?

Published on 14 Nov 2014 - 4:49

score 142 · Answer 15 · 2026-04-02 05:30:59

142

Views

Convergence test for improper multiple integral

Published on 02 Apr 2026 - 5:30

List Question

How do you evaluate an exponential term that contains both $-\infty$ and $+\infty$?

A strange integral: $\int_{-\infty}^{+\infty} {dx \over 1 + \left(x + \tan x\right)^2} = \pi.$

How to evaluate this improper integral?

Does $\sum \frac{(n+4^n)}{n+6^n}$ converge or diverge?

Closed form of $\int_{0}^{\infty} \frac{\tanh(x)\,\tanh(2x)}{x^2}\;dx$

Integral of $\int_0^{\infty} x^{4n+3} e^{-x} \sin x dx$.

Determine how large the number a has to be?

Evaluating a specific definite integral

Can this divergent integral transform be regularized?

show $\int^\infty_0 e^{-sx} x^{-1} \sin{x} dx = \frac14 \log{(1+4s^{-2})}$ for $s>0$

Divergence of double integral $\iint_{x^2 + y^2 \leq 1} \frac{\mathop{d}x\mathop{d}y}{(x^2 + xy + y^2)^p},\quad p \geq 1$

Orthogonality of Hermite functions

Convergence of $ \int_2^\infty \frac{1}{x^q(\ln x)^p} dx $

Is $\int_0^{\pi/2} \sin^a(\theta)\tan(\theta) d\theta $ convergent?

Convergence test for improper multiple integral

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