Question

$\int_0^1\frac{(f(x)-1)^2 -4x^2}{x^{3.5}}\,dx$ exists. Calculate $f(0)$ and $f'(0)$

score 94 · Answer 1 · 2026-04-17 11:34:03

94

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$\int_0^1\frac{(f(x)-1)^2 -4x^2}{x^{3.5}}\,dx$ exists. Calculate $f(0)$ and $f'(0)$

Published on 17 Apr 2026 - 11:34

score 62 · Answer 2 · 2026-04-14 22:53:34

62

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Convergence of $\int_0^1 \sqrt[3]{\ln(1/x)} \mathrm{d}x $

Published on 14 Apr 2026 - 22:53

score 2.5k · Answer 3 · 2026-04-16 03:53:46

2.5k

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Convergence of $\int_0^\infty \sin(t)/t^\gamma \mathrm{d}t$

Published on 16 Apr 2026 - 3:53

score 71.8k · Answer 4 · 2026-04-15 00:39:26

71.8k

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Improper integral $\sin(x)/x $ converges absolutely, conditionally or diverges?

Published on 15 Apr 2026 - 0:39

score 2.9k · Answer 5 · 2026-04-17 03:30:27

2.9k

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An integral involving Fresnel integrals $\int_0^\infty \left(\left(2\ S(x)-1\right)^2+\left(2\ C(x)-1\right)^2\right)^2 x\ \mathrm dx,$

Published on 17 Apr 2026 - 3:30

score 13.2k · Answer 6 · 2026-04-12 04:35:56

13.2k

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Integrating $\int^{\infty}_0 e^{-x^2}\,dx$ using Feynman's parametrization trick

Published on 12 Apr 2026 - 4:35

score 105 · Answer 7 · 2026-04-16 03:51:33

105

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What is $\int_{-\infty}^{\infty} \frac{e^{-\alpha t} \cos[t + y]}{1+\beta e^{-2\alpha t} } dt$?

Published on 16 Apr 2026 - 3:51

score 16.4k · Answer 8 · 2026-04-16 22:29:41

16.4k

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Approximation of alternating series $\sum_{n=1}^\infty a_n = 0.55 - (0.55)^3/3! + (0.55)^5/5! - (0.55)^7/7! + ...$

Published on 16 Apr 2026 - 22:29

score 1.5k · Answer 9 · 2026-04-17 05:38:25

1.5k

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Find the value of $\int_0^{\infty}\frac{x^3}{(x^4+1)(e^x-1)}\mathrm dx$

Published on 17 Apr 2026 - 5:38

score 78 · Answer 10 · 2026-04-17 12:35:35

78

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Test of convergence of $\int_{-\infty}^{\infty} \dfrac{x^6+6}{x^8+8}dx$

Published on 17 Apr 2026 - 12:35

score 855 · Answer 11 · 2026-04-15 18:09:58

855

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Complex-valued Fourier integral: $ \int_{ - \infty }^{ + \infty } {\frac{{\cos (ax)}}{{{x^2} + 1}}{e^{ - ibx}}\,\mathrm dx} $

Published on 15 Apr 2026 - 18:09

score 588 · Answer 12 · 2026-04-16 19:36:33

588

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$\int_0^\infty(\log x)^2(\mathrm{sech}\,x)^2\mathrm dx$

Published on 16 Apr 2026 - 19:36

score 229 · Answer 13 · 2026-04-16 01:22:28

229

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Integral of a rational function: Proof of $\sqrt{C}\,\int_{0}^{+\infty }{{{y^2}\over{y^2\,C+y^4-2\,y^2+1}}\;\mathrm dy}= {{\pi}\over{2}}$?

Published on 16 Apr 2026 - 1:22

score 95 · Answer 14 · 2026-04-16 10:47:14

95

Views

Test for convergence for improper integral $1/x^x$

Published on 16 Apr 2026 - 10:47

score 251 · Answer 15 · 2026-04-13 10:20:07

251

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Please help finishing the calculation to find the Entropy of Pareto distribution.

Published on 13 Apr 2026 - 10:20

List Question

$\int_0^1\frac{(f(x)-1)^2 -4x^2}{x^{3.5}}\,dx$ exists. Calculate $f(0)$ and $f'(0)$

Convergence of $\int_0^1 \sqrt[3]{\ln(1/x)} \mathrm{d}x $

Convergence of $\int_0^\infty \sin(t)/t^\gamma \mathrm{d}t$

Improper integral $\sin(x)/x $ converges absolutely, conditionally or diverges?

An integral involving Fresnel integrals $\int_0^\infty \left(\left(2\ S(x)-1\right)^2+\left(2\ C(x)-1\right)^2\right)^2 x\ \mathrm dx,$

Integrating $\int^{\infty}_0 e^{-x^2}\,dx$ using Feynman's parametrization trick

What is $\int_{-\infty}^{\infty} \frac{e^{-\alpha t} \cos[t + y]}{1+\beta e^{-2\alpha t} } dt$?

Approximation of alternating series $\sum_{n=1}^\infty a_n = 0.55 - (0.55)^3/3! + (0.55)^5/5! - (0.55)^7/7! + ...$

Find the value of $\int_0^{\infty}\frac{x^3}{(x^4+1)(e^x-1)}\mathrm dx$

Test of convergence of $\int_{-\infty}^{\infty} \dfrac{x^6+6}{x^8+8}dx$

Complex-valued Fourier integral: $ \int_{ - \infty }^{ + \infty } {\frac{{\cos (ax)}}{{{x^2} + 1}}{e^{ - ibx}}\,\mathrm dx} $

$\int_0^\infty(\log x)^2(\mathrm{sech}\,x)^2\mathrm dx$

Integral of a rational function: Proof of $\sqrt{C}\,\int_{0}^{+\infty }{{{y^2}\over{y^2\,C+y^4-2\,y^2+1}}\;\mathrm dy}= {{\pi}\over{2}}$?

Test for convergence for improper integral $1/x^x$

Please help finishing the calculation to find the Entropy of Pareto distribution.

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