Question

Proving that $\int_{0}^{1}\frac{\sin^{2}x}{x^{1+\alpha}}dx<\infty$ for $\alpha\in(0,2)$

score 75 · Answer 1 · 2026-03-26 02:47:54

75

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Proving that $\int_{0}^{1}\frac{\sin^{2}x}{x^{1+\alpha}}dx<\infty$ for $\alpha\in(0,2)$

Published on 26 Mar 2026 - 2:47

score 101 · Answer 2 · 2026-03-25 01:18:47

101

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Integral inequality $e^{\int _0^1f\left(x\right)dx-1\:}\le \frac{1}{4}\int _0^1\left(x+1\right)e^{f\left(x\right)}dx$

Published on 25 Mar 2026 - 1:18

score 121 · Answer 3 · 2026-03-29 03:28:08

121

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Prove that the sequence $a_n = \int_1^2 \sqrt[n]{{e}^{x^2}}\, dx$ converge

Published on 29 Mar 2026 - 3:28

score 165 · Answer 4 · 2026-04-09 20:07:42

165

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Recurrence relation for integral

Published on 09 Apr 2026 - 20:07

score 234 · Answer 5 · 2018-03-03 03:25:31

234

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Definite Integral Problem up-to infinity

Published on 03 Mar 2018 - 3:25

score 83 · Answer 6 · 2026-04-11 04:23:23

83

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Integration of $\tan(\frac1x)$

Published on 11 Apr 2026 - 4:23

score 86 · Answer 7 · 2018-03-03 10:24:13

86

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integration by parts in definite integral

Published on 03 Mar 2018 - 10:24

score 235 · Answer 8 · 2026-03-24 23:44:29

235

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Integration problem involving $\sqrt{\cos(x)-\cos^3(x)}$

Published on 24 Mar 2026 - 23:44

score 96 · Answer 9 · 2018-03-03 17:54:16

96

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Integral limit $\lim _{t\to 0}\frac 1 t \int_0^1 (f(x+t)-f(x))x \, dx$

Published on 03 Mar 2018 - 17:54

score 69 · Answer 10 · 2018-03-03 19:46:42

69

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Calculate area between pair of curves $y+x=2$ and $y^2=2(2-x)$. please help

Published on 03 Mar 2018 - 19:46

score 102 · Answer 11 · 2026-03-29 17:24:47

102

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$\lim_{n\to\infty}\int_0^1\sin (2 \pi nx)\, \mathrm{e}^{-\sqrt{x}}dx=0$

Published on 29 Mar 2026 - 17:24

score 508 · Answer 12 · 2026-04-06 06:59:38

508

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Find integral of composition of functions

Published on 06 Apr 2026 - 6:59

score 141 · Answer 13 · 2026-04-02 05:07:11

141

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Prove that $\int_{2017}^{2018} (\arctan(\ln(x))-\ln(\arctan(x)))\,\mathrm dx>0$

Published on 02 Apr 2026 - 5:07

score 34 · Answer 14 · 2018-03-04 09:30:20

34

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Integrals reductive forms

Published on 04 Mar 2018 - 9:30

score 205 · Answer 15 · 2018-03-04 11:37:21

205

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Evaluating $\int_{0}^{1} \frac{\ln(x)}{\sqrt{1-x}} dx$ using different methods

Published on 04 Mar 2018 - 11:37

List Question

Proving that $\int_{0}^{1}\frac{\sin^{2}x}{x^{1+\alpha}}dx<\infty$ for $\alpha\in(0,2)$

Integral inequality $e^{\int _0^1f\left(x\right)dx-1\:}\le \frac{1}{4}\int _0^1\left(x+1\right)e^{f\left(x\right)}dx$

Prove that the sequence $a_n = \int_1^2 \sqrt[n]{{e}^{x^2}}\, dx$ converge

Recurrence relation for integral

Definite Integral Problem up-to infinity

Integration of $\tan(\frac1x)$

integration by parts in definite integral

Integration problem involving $\sqrt{\cos(x)-\cos^3(x)}$

Integral limit $\lim _{t\to 0}\frac 1 t \int_0^1 (f(x+t)-f(x))x \, dx$

Calculate area between pair of curves $y+x=2$ and $y^2=2(2-x)$. please help

$\lim_{n\to\infty}\int_0^1\sin (2 \pi nx)\, \mathrm{e}^{-\sqrt{x}}dx=0$

Find integral of composition of functions

Prove that $\int_{2017}^{2018} (\arctan(\ln(x))-\ln(\arctan(x)))\,\mathrm dx>0$

Integrals reductive forms

Evaluating $\int_{0}^{1} \frac{\ln(x)}{\sqrt{1-x}} dx$ using different methods

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