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5h
revised Evaluate $ \int_{0}^{1} \ln(x)\ln(1-x)\,dx $
I reorganized my answer and added a link.
6h
comment A reason for the value of $\int_{0}^{1}\log{(x)}\log{(1-x)}\,\mathrm{d}x$
related: math.stackexchange.com/questions/917833/…
Aug
26
comment Calculating $\int_0^{\infty } \left(\text{Li}_2\left(-\frac{1}{x^2}\right)\right)^2 \, dx$
Very creative approach. +1
Aug
26
revised Calculating $\int_0^{\infty } \left(\text{Li}_2\left(-\frac{1}{x^2}\right)\right)^2 \, dx$
deleted 45 characters in body
Aug
26
revised Calculating $\int_0^{\infty } \left(\text{Li}_2\left(-\frac{1}{x^2}\right)\right)^2 \, dx$
deleted 45 characters in body
Aug
26
answered Calculating $\int_0^{\infty } \left(\text{Li}_2\left(-\frac{1}{x^2}\right)\right)^2 \, dx$
Aug
25
revised Integral $\int_{-\infty}^{\infty}\frac{e^{r \arctan(ax)}+e^{-r \arctan(ax)}}{1+x^2}\cos \left( \frac{r}{2}\log(1+a^2x^2)\right)dx$
deleted 41 characters in body
Aug
24
revised Integral $\int_{-\infty}^{\infty}\frac{e^{r \arctan(ax)}+e^{-r \arctan(ax)}}{1+x^2}\cos \left( \frac{r}{2}\log(1+a^2x^2)\right)dx$
I corrected the necessary conditions, and I converted the post to a community wiki.
Aug
24
revised Integral $\int_{-\infty}^{\infty}\frac{e^{r \arctan(ax)}+e^{-r \arctan(ax)}}{1+x^2}\cos \left( \frac{r}{2}\log(1+a^2x^2)\right)dx$
I improved the question slightly.
Aug
21
awarded  Necromancer
Aug
15
revised Integral $\int_0^1 \ln(x)^n \operatorname{Ei}(x) \, dx$
added 281 characters in body
Aug
15
revised Integral $\int_0^1 \ln(x)^n \operatorname{Ei}(x) \, dx$
added 4 characters in body
Aug
15
revised Integral $\int_0^1 \ln(x)^n \operatorname{Ei}(x) \, dx$
added 9 characters in body
Aug
15
revised Integral $\int_0^1 \ln(x)^n \operatorname{Ei}(x) \, dx$
deleted 1 character in body
Aug
15
answered Integral $\int_0^1 \ln(x)^n \operatorname{Ei}(x) \, dx$
Aug
14
revised Branch points of $\log (\tan z)$
added 545 characters in body; edited title
Aug
13
comment Fourier transform of $\Gamma \left (\frac{1}{2}-i \frac{p}{2 \pi} \right) /\sqrt{ \cosh(p/2)}$
In robjohn's answer, he has a branch cut on $[\frac{\pi}{2}, \infty)$ and a branch cut on $(-\infty, -\frac{\pi}{2}]$. The equivalent cuts here would be $[\frac{i \pi}{2}, i\infty)$ and $(-i\infty, -\frac{i \pi}{2}]$. But in your answer you appear to be circling around pairs of branch points. And I don't think $f(z,x)$ remains well-defined if you do that.
Aug
13
comment Fourier transform of $\Gamma \left (\frac{1}{2}-i \frac{p}{2 \pi} \right) /\sqrt{ \cosh(p/2)}$
I could be mistaken, but since $\log (\cosh)$ can be defined by integrating $\tanh z$ on the complex plane from the origin to $z$, I don't think $\frac{1}{\cosh^{3/2}(z)}$ (and thus $f(z,x)$) is well-defined if just the line segments between the branch points are omitted.
Aug
12
revised A definite integral with tanh and sin
I corrected two sign errors.
Aug
12
revised A definite integral with tanh and sin
I tried to improve the question a bit.