query: Finding a closed form for $\int_{0}^{1}\frac{\ln\left ( 1-x^{2} \right )\arcsin ^{2}x}{x^{2}}\mathrm{d}x\approx -0.939332$
positive_passages.docid: 93610
positive_passages.text: What is $\int_0^1 \frac{\log \left(1-x^2\right) \sin ^{-1}(x)^2}{x^2} \, dx$?
negative_passages.docid: 107119
negative_passages.text: A logarithmic integral $\int^1_0 \frac{\log\left(\frac{1+x}{1-x}\right)}{x\sqrt{1-x^2}}\,dx$
negative_passages.docid: 45841
negative_passages.text: integral of $\int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx$ using contour integration?
negative_passages.docid: 101045
negative_passages.text: Is there a closed form for the integral $\int_0^1 x^n \log^m (1-x) \, {\rm d}x$?
negative_passages.docid: 12423
negative_passages.text: "Closed" form for $\sum \frac{1}{n^n}$
negative_passages.docid: 115198
negative_passages.text: Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$
negative_passages.docid: 68241
negative_passages.text: Integral $\int_0^1 \frac{\ln(1-x)\ln(1+x^2)}{x}dx$
negative_passages.docid: 80553
negative_passages.text: Show that,$\int_0^\pi \left|\frac{\sin nx}{x}\right|\mathrm{d}x \ge \frac{2}{\pi}\left(1+\frac12+\cdots+\frac{1}{n}\right)$
negative_passages.docid: 142516
negative_passages.text: Evaluating the integral, $\int_{0}^{\infty} \ln\left(1 - e^{-x}\right) \,\mathrm dx $
negative_passages.docid: 5537
negative_passages.text: Closed form for $ \int_0^\infty {\frac{{{x^n}}}{{1 + {x^m}}}dx }$
negative_passages.docid: 74241
negative_passages.text: Integrate square of the log-sine integral: $\int_0^{\frac{\pi}{2}}\ln^{2}(\sin(x))dx$
negative_passages.docid: 96505
negative_passages.text: Compute $\int_0^\infty \left(\frac{1}{x}\right)^{\ln(x)}\,\mathrm{d}x$
negative_passages.docid: 147977
negative_passages.text: Evaluate $\int_0^1\left(\frac{x-1}{x+1}\right)^n\frac{1}{\ln x} \,dx$
negative_passages.docid: 133160
negative_passages.text: Closed form for $\int_0^\infty\frac{1}{(1+x^2)^s}\,dx$ when $s\in (0.5,\infty)\setminus\mathbb{N}$
negative_passages.docid: 68504
negative_passages.text: Compute $\int_0^1 \frac{\arcsin(x)}{x}dx$
negative_passages.docid: 150200
negative_passages.text: finding $\lim_{n\rightarrow\infty}\sum_{r=1}^{n}\arctan\left(\frac{2r}{1-r^2+r^4}\right)$
negative_passages.docid: 24182
negative_passages.text: Evaluating $\int_{0}^{\infty}\frac{\sin^{2n+1}x}{x}\mathrm{d}x$