Question

Integral of $ x \ln( \sin (x))$ from 0 to $ \pi $

score 7.6k · Answer 1 · 2026-04-13 22:19:02

7.6k

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Integral of $ x \ln( \sin (x))$ from 0 to $ \pi $

Published on 13 Apr 2026 - 22:19

score 133 · Answer 2 · 2026-04-16 21:13:08

133

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Show that $\int_1^\infty \frac{\ln x}{\left(1+x^2\right)^\lambda}\mathrm dx$ is convergent only for $\lambda > \frac{1}{2}$

Published on 16 Apr 2026 - 21:13

score 168 · Answer 3 · 2026-04-17 11:35:25

168

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Integrate $\frac{1}{\sqrt{1-x^4}}$ from $0$ to $1$.

Published on 17 Apr 2026 - 11:35

score 1k · Answer 4 · 2026-04-15 20:27:18

1k

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Finding $\int_{-\infty}^\infty \frac{x^2}{x^4+1}\;dx$

Published on 15 Apr 2026 - 20:27

score 101 · Answer 5 · 2026-04-16 06:26:27

101

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Proving that $\lim_{x \to\infty}\int_{x}^{x+1} f(t) dt=0$ if $\int_{1}^{\infty}f(x)<\infty$

Published on 16 Apr 2026 - 6:26

score 134 · Answer 6 · 2026-04-17 04:17:29

134

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Analysis: Prove that this improper integral diverges but the limit as $t \rightarrow \infty=\pi$?

Published on 17 Apr 2026 - 4:17

score 30 · Answer 7 · 2026-04-17 07:43:53

30

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Does $\int^{\infty}_2 {e^{x/4} \over x^3({\ln x})^5} $ converge?

Published on 17 Apr 2026 - 7:43

score 94 · Answer 8 · 2026-04-11 02:50:06

94

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Finding a dominating function to evaluate arctan integral

Published on 11 Apr 2026 - 2:50

score 85 · Answer 9 · 2026-03-29 10:55:47

85

Views

Help with improper integrals containing partial fractions

Published on 29 Mar 2026 - 10:55

score 256 · Answer 10 · 2026-04-14 19:04:40

256

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Closed-form solution of the integral $\int_{0}^{\infty}\frac{\ln(1+x)}{(1+ax)^{(1+m)}}\,dx$

Published on 14 Apr 2026 - 19:04

score 79 · Answer 11 · 2026-04-14 22:09:16

79

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Diverging integrals less than |sin(x)/x| (A Dirichlet Integral)

Published on 14 Apr 2026 - 22:09

score 137 · Answer 12 · 2026-04-10 18:10:49

137

Views

Integral from $\infty$ to $\infty$

Published on 10 Apr 2026 - 18:10

score 16 · Answer 13 · 2026-03-08 06:45:48

16

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Splitting a complex controur integration in two. Figuring out the orientation.

Published on 08 Mar 2026 - 6:45

score 685 · Answer 14 · 2026-04-28 00:04:10

685

Views

Is $f(x)=\frac{\sqrt{1-x}}{\ln{x}}$ on $[0,1]$ a Lebesgue-integrable function?

Published on 28 Apr 2026 - 0:04

score 785 · Answer 15 · 2026-04-16 04:26:02

785

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If $f$ is positive, decreasing, and continuous on $[0,+\infty)$ show that $\int_0^\infty f(t)dt$ converges iff $\sum_{n=0}^\infty f(n)$ converges

Published on 16 Apr 2026 - 4:26

List Question

Integral of $ x \ln( \sin (x))$ from 0 to $ \pi $

Show that $\int_1^\infty \frac{\ln x}{\left(1+x^2\right)^\lambda}\mathrm dx$ is convergent only for $\lambda > \frac{1}{2}$

Integrate $\frac{1}{\sqrt{1-x^4}}$ from $0$ to $1$.

Finding $\int_{-\infty}^\infty \frac{x^2}{x^4+1}\;dx$

Proving that $\lim_{x \to\infty}\int_{x}^{x+1} f(t) dt=0$ if $\int_{1}^{\infty}f(x)<\infty$

Analysis: Prove that this improper integral diverges but the limit as $t \rightarrow \infty=\pi$?

Does $\int^{\infty}_2 {e^{x/4} \over x^3({\ln x})^5} $ converge?

Finding a dominating function to evaluate arctan integral

Help with improper integrals containing partial fractions

Closed-form solution of the integral $\int_{0}^{\infty}\frac{\ln(1+x)}{(1+ax)^{(1+m)}}\,dx$

Diverging integrals less than |sin(x)/x| (A Dirichlet Integral)

Integral from $\infty$ to $\infty$

Splitting a complex controur integration in two. Figuring out the orientation.

Is $f(x)=\frac{\sqrt{1-x}}{\ln{x}}$ on $[0,1]$ a Lebesgue-integrable function?

If $f$ is positive, decreasing, and continuous on $[0,+\infty)$ show that $\int_0^\infty f(t)dt$ converges iff $\sum_{n=0}^\infty f(n)$ converges

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