Question

Can $\int_{-\infty}^{\infty} C(1+x^2)^{-m} \,\mathrm dx$ be evaluated without trig substitution?

score 231 · Answer 1 · 2026-04-16 03:41:40

231

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Can $\int_{-\infty}^{\infty} C(1+x^2)^{-m} \,\mathrm dx$ be evaluated without trig substitution?

Published on 16 Apr 2026 - 3:41

score 1.1k · Answer 2 · 2026-05-05 20:26:48

1.1k

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Computing the Gaussian integral with step functions

Published on 05 May 2026 - 20:26

score 6.5k · Answer 3 · 2026-04-16 02:18:49

6.5k

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Evaluating $\int_0^\infty \frac{dx}{1+x^4}$.

Published on 16 Apr 2026 - 2:18

score 117 · Answer 4 · 2026-04-14 06:40:12

117

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Prove the identity $\intop_\rho^a \frac{\arcsin \frac{x}{a}}{\sqrt{x^2-\rho^2}}\mathbb{d}x=\frac{\pi}{2}\ln \frac{a+\sqrt{a^2-\rho^2}}{a}$

Published on 14 Apr 2026 - 6:40

score 193 · Answer 5 · 2026-04-10 11:20:15

193

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How to solve this integral? - A Proof is needed

Published on 10 Apr 2026 - 11:20

score 612 · Answer 6 · 2026-04-17 02:47:20

612

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Evaluate ${\int_0^\infty e^{-t} \log(\cos^2 t)}\,\mathrm dt$

Published on 17 Apr 2026 - 2:47

score 636 · Answer 7 · 2026-04-15 13:33:23

636

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Improper integral - show convergence/divergence

Published on 15 Apr 2026 - 13:33

score 88 · Answer 8 · 2026-04-20 02:18:12

88

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$\int_{0}^{\infty}{\ln(x+3){x^{-2}} \mathrm d x}$ converges?

Published on 20 Apr 2026 - 2:18

score 272 · Answer 9 · 2026-04-17 00:10:37

272

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integral involving modified bessel

Published on 17 Apr 2026 - 0:10

score 3.2k · Answer 10 · 2026-04-15 02:35:20

3.2k

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Prove $\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$ using real analysis techniques only

Published on 15 Apr 2026 - 2:35

score 134 · Answer 11 · 2026-04-17 11:54:48

134

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divergence of $\int_{2}^{\infty}\frac{dx}{x^{2}-x-2}$

Published on 17 Apr 2026 - 11:54

score 23.4k · Answer 12 · 2026-04-11 12:35:59

23.4k

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Laplace transform of sin(at)

Published on 11 Apr 2026 - 12:35

score 1.4k · Answer 13 · 2026-04-16 08:08:10

1.4k

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Show that $\int_{0}^{\infty }\frac {\ln x}{x^4+1}\ dx =-\frac{\pi^2 \sqrt{2}}{16}$

Published on 16 Apr 2026 - 8:08

score 153 · Answer 14 · 2026-04-08 20:11:31

153

Views

Taking an integral of e^(another integral) with respect to the limit of integration of (another integral)

Published on 08 Apr 2026 - 20:11

score 1.3k · Answer 15 · 2026-04-16 13:23:37

1.3k

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Conditional or absolute convergence of an integral $\int_{0}^{\infty}\frac{\sin x}{1+x^{2}}dx$

Published on 16 Apr 2026 - 13:23

List Question

Can $\int_{-\infty}^{\infty} C(1+x^2)^{-m} \,\mathrm dx$ be evaluated without trig substitution?

Computing the Gaussian integral with step functions

Evaluating $\int_0^\infty \frac{dx}{1+x^4}$.

Prove the identity $\intop_\rho^a \frac{\arcsin \frac{x}{a}}{\sqrt{x^2-\rho^2}}\mathbb{d}x=\frac{\pi}{2}\ln \frac{a+\sqrt{a^2-\rho^2}}{a}$

How to solve this integral? - A Proof is needed

Evaluate ${\int_0^\infty e^{-t} \log(\cos^2 t)}\,\mathrm dt$

Improper integral - show convergence/divergence

$\int_{0}^{\infty}{\ln(x+3){x^{-2}} \mathrm d x}$ converges?

integral involving modified bessel

Prove $\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$ using real analysis techniques only

divergence of $\int_{2}^{\infty}\frac{dx}{x^{2}-x-2}$

Laplace transform of sin(at)

Show that $\int_{0}^{\infty }\frac {\ln x}{x^4+1}\ dx =-\frac{\pi^2 \sqrt{2}}{16}$

Taking an integral of e^(another integral) with respect to the limit of integration of (another integral)

Conditional or absolute convergence of an integral $\int_{0}^{\infty}\frac{\sin x}{1+x^{2}}dx$

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