Question

Proof for divergence of $\int_1^\infty \cos(x^\frac{3}{4})$

score 233 · Answer 1 · 2026-04-16 13:01:10

233

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Proof for divergence of $\int_1^\infty \cos(x^\frac{3}{4})$

Published on 16 Apr 2026 - 13:01

score 124 · Answer 2 · 2026-04-17 10:50:51

124

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How to solve $\int_0^{\infty}\frac{x^n}{(x^2+1)^n}\,\mathrm dx$ for $n\ge 2$?

Published on 17 Apr 2026 - 10:50

score 120 · Answer 3 · 2026-04-15 23:28:23

120

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To show that: $\int_{-1}^{1} \frac{1}{(1+x)^{1/3}\ (1-x)^{2/3}} dx = \frac{2\pi}{\sqrt3}$

Published on 15 Apr 2026 - 23:28

score 422 · Answer 4 · 2026-04-12 09:41:47

422

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Other ways to compute this integral?

Published on 12 Apr 2026 - 9:41

score 142 · Answer 5 · 2026-04-12 03:13:42

142

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How do I evaluate the following integral $\int_{-\infty}^\infty\mathop{dx} \frac{x^n}{(x^2+a^2)^m}$?

Published on 12 Apr 2026 - 3:13

score 268 · Answer 6 · 2026-04-01 04:23:20

268

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Integral of Dirac Delta Function

Published on 01 Apr 2026 - 4:23

score 19 · Answer 7 · 2026-04-12 18:26:49

19

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Determine integral range in function of 2 random variables.

Published on 12 Apr 2026 - 18:26

score 84 · Answer 8 · 2026-04-17 04:28:58

84

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Determining convergence of improper integrals including $ \int_{0} ^ {1} \frac{\ln\left(1+e^x\right)-x}{x^2}\text{d}x $

Published on 17 Apr 2026 - 4:28

score 57 · Answer 9 · 2026-04-17 04:01:25

57

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Solving integral $\int_{-\infty}^{\infty}\frac{e^{-(2\pi-i2\pi t) f}}{(3+i2\pi f)^2}df$

Published on 17 Apr 2026 - 4:01

score 2.9k · Answer 10 · 2026-04-17 11:52:53

2.9k

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Determine whether the integral is convergent or divergent. $\int^{\infty}_1 81\frac{\ln(x)}{x}dx$

Published on 17 Apr 2026 - 11:52

score 112 · Answer 11 · 2026-04-11 13:17:22

112

Views

Integral involving an exponential and logarithmic function

Published on 11 Apr 2026 - 13:17

score 68 · Answer 12 · 2026-04-16 02:28:15

68

Views

If $f$ is continuous on [0,$∞$) and $\lim_{x\to\infty} f(x)= 0$, then prove that $\int_{0}^{∞} f'(x) dx = -f(0).$

Published on 16 Apr 2026 - 2:28

score 91 · Answer 13 · 2026-04-12 05:14:11

91

Views

How do I evaluate the following Integral

Published on 12 Apr 2026 - 5:14

score 42 · Answer 14 · 2026-04-09 11:42:50

42

Views

Singularity of an oscillatory integral

Published on 09 Apr 2026 - 11:42

score 61 · Answer 15 · 2026-04-16 17:54:07

61

Views

Integrating $f(x,y)= \frac{1}{2 \pi (t-s)s} e^{- \frac{(y-x)^2}{2(t-s)}- \frac{x^2}{2s}}$

Published on 16 Apr 2026 - 17:54

List Question

Proof for divergence of $\int_1^\infty \cos(x^\frac{3}{4})$

How to solve $\int_0^{\infty}\frac{x^n}{(x^2+1)^n}\,\mathrm dx$ for $n\ge 2$?

To show that: $\int_{-1}^{1} \frac{1}{(1+x)^{1/3}\ (1-x)^{2/3}} dx = \frac{2\pi}{\sqrt3}$

Other ways to compute this integral?

How do I evaluate the following integral $\int_{-\infty}^\infty\mathop{dx} \frac{x^n}{(x^2+a^2)^m}$?

Integral of Dirac Delta Function

Determine integral range in function of 2 random variables.

Determining convergence of improper integrals including $ \int_{0} ^ {1} \frac{\ln\left(1+e^x\right)-x}{x^2}\text{d}x $

Solving integral $\int_{-\infty}^{\infty}\frac{e^{-(2\pi-i2\pi t) f}}{(3+i2\pi f)^2}df$

Determine whether the integral is convergent or divergent. $\int^{\infty}_1 81\frac{\ln(x)}{x}dx$

Integral involving an exponential and logarithmic function

If $f$ is continuous on [0,$∞$) and $\lim_{x\to\infty} f(x)= 0$, then prove that $\int_{0}^{∞} f'(x) dx = -f(0).$

How do I evaluate the following Integral

Singularity of an oscillatory integral

Integrating $f(x,y)= \frac{1}{2 \pi (t-s)s} e^{- \frac{(y-x)^2}{2(t-s)}- \frac{x^2}{2s}}$

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