Question

Is there other simple way to evaluate $\int_0^1 \frac{\ln^p x}{1-x^n} d x$ if $p\in \mathbb N$ and $n>0$?

score 110 · Answer 1 · 2026-03-28 22:29:55

110

Views

Is there other simple way to evaluate $\int_0^1 \frac{\ln^p x}{1-x^n} d x$ if $p\in \mathbb N$ and $n>0$?

Published on 28 Mar 2026 - 22:29

score 167 · Answer 2 · 2026-04-02 18:43:41

167

Views

Is there any other simple method to evaluate $\int_0^{1} \frac{\ln ^n x}{\left(1-x^2\right)^2}dx $?

Published on 02 Apr 2026 - 18:43

score 175 · Answer 3 · 2026-03-28 22:30:00

175

Views

Can $\int_0^{\infty} \frac{\ln ^n x}{\left(1-x^2\right)^2} d x$ be expressed in terms of the zeta function of an even integer?

Published on 28 Mar 2026 - 22:30

score 76 · Answer 4 · 2023-02-15 21:48:59

76

Views

For which $p$ does $\int_0^1 x^p(x+1)\log x \ dx $ converge?

Published on 15 Feb 2023 - 21:48

score 200 · Answer 5 · 2023-02-17 13:14:01

200

Views

Convergence of integral: $\displaystyle\mathcal I=\int_0^1\frac{\sin^3(1/x)\cos(1/x)}{x^{3/2}+x^2\ln(1+1/x)}dx$

Published on 17 Feb 2023 - 13:14

score 37 · Answer 6 · 2026-04-13 16:37:46

37

Views

Does (sin(1/x))^2 have an improper integral in between -inf and inf

Published on 13 Apr 2026 - 16:37

score 85 · Answer 7 · 2026-04-12 21:13:56

85

Views

Improper Integral on $p$ values

Published on 12 Apr 2026 - 21:13

score 303 · Answer 8 · 2026-04-08 03:19:02

303

Views

Evaluate the Integral $\int_{0}^{\infty}\ln\left(1+\pi\frac{2\cosh\left(t\right)+\pi}{t^{2}+\cosh\left(t\right)^{2}}\right)dt$

Published on 08 Apr 2026 - 3:19

score 287 · Answer 9 · 2026-04-07 19:32:46

287

Views

Evaluating $\int_{-\infty}^{\infty}\frac{\ln\left(\frac{1}{2}+x+x^{2}\right)}{1+x^{2}}dx$

Published on 07 Apr 2026 - 19:32

score 110 · Answer 10 · 2026-03-30 07:09:09

110

Views

Evaluating the improper integral $\int_0^\infty k^3\left(k+\sqrt{k^2+\alpha^2}\right)e^{-\beta\left(k+\sqrt{k^2+\alpha^2}\right)}J_0(\rho k)\text{d}k$

Published on 30 Mar 2026 - 7:09

score 365 · Answer 11 · 2023-02-21 23:50:42

365

Views

Putnam, A3 (2016)

Published on 21 Feb 2023 - 23:50

score 117 · Answer 12 · 2026-03-29 00:00:03

117

Views

Computing $\int_0^{\infty} x^n\left\lfloor\frac{1}{x}\right\rfloor d x=\frac{\zeta(n+1)}{n+1}$, where $n\in \mathbb N$.

Published on 29 Mar 2026 - 0:00

score 702 · Answer 13 · 2023-02-23 05:45:22

702

Views

Integral that gives one or minus one

Published on 23 Feb 2023 - 5:45

score 83 · Answer 14 · 2026-04-12 23:25:30

83

Views

About the convergence of the particular type of improper integral

Published on 12 Apr 2026 - 23:25

score 412 · Answer 15 · 2023-02-23 19:41:05

412

Views

Compute the integral $\int_{-\infty}^\infty \frac{\sin(x) (1+\cos(x))}{x(2+\cos(x))} dx$

Published on 23 Feb 2023 - 19:41

List Question

Is there other simple way to evaluate $\int_0^1 \frac{\ln^p x}{1-x^n} d x$ if $p\in \mathbb N$ and $n>0$?

Is there any other simple method to evaluate $\int_0^{1} \frac{\ln ^n x}{\left(1-x^2\right)^2}dx $?

Can $\int_0^{\infty} \frac{\ln ^n x}{\left(1-x^2\right)^2} d x$ be expressed in terms of the zeta function of an even integer?

For which $p$ does $\int_0^1 x^p(x+1)\log x \ dx $ converge?

Convergence of integral: $\displaystyle\mathcal I=\int_0^1\frac{\sin^3(1/x)\cos(1/x)}{x^{3/2}+x^2\ln(1+1/x)}dx$

Does (sin(1/x))^2 have an improper integral in between -inf and inf

Improper Integral on $p$ values

Evaluate the Integral $\int_{0}^{\infty}\ln\left(1+\pi\frac{2\cosh\left(t\right)+\pi}{t^{2}+\cosh\left(t\right)^{2}}\right)dt$

Evaluating $\int_{-\infty}^{\infty}\frac{\ln\left(\frac{1}{2}+x+x^{2}\right)}{1+x^{2}}dx$

Evaluating the improper integral $\int_0^\infty k^3\left(k+\sqrt{k^2+\alpha^2}\right)e^{-\beta\left(k+\sqrt{k^2+\alpha^2}\right)}J_0(\rho k)\text{d}k$

Putnam, A3 (2016)

Computing $\int_0^{\infty} x^n\left\lfloor\frac{1}{x}\right\rfloor d x=\frac{\zeta(n+1)}{n+1}$, where $n\in \mathbb N$.

Integral that gives one or minus one

About the convergence of the particular type of improper integral

Compute the integral $\int_{-\infty}^\infty \frac{\sin(x) (1+\cos(x))}{x(2+\cos(x))} dx$

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