query: How to compute the integral $\int_0^1 \frac{x\ln x}{\ln (1-x)}dx$?
positive_passages.docid: 152860
positive_passages.text: How to evalute $\int_{0}^{1}\frac{x\log x}{\log(1-x)}dx$
negative_passages.docid: 51216
negative_passages.text: Different ways to tackle the integral $\int_0^1\sqrt\frac x{1-x}\,dx$
negative_passages.docid: 102399
negative_passages.text: Computing $ \int_0^\infty \frac{\log x}{\exp x} \ dx $
negative_passages.docid: 114195
negative_passages.text: Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$
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: 109901
negative_passages.text: Computing $\int_0^\infty\frac1{(x+1)(x+2)\cdots(x+n)}\mathrm dx $
negative_passages.docid: 132388
negative_passages.text: Calculate $I=\int_0^1\frac{\ln(1+x)}{1+x^2}\,dx$
negative_passages.docid: 119572
negative_passages.text: Finding the integral of $\frac{x}{e^x + 1}$
negative_passages.docid: 146349
negative_passages.text: $\int_0^\infty \frac{\ln\left(1+x-\sqrt{2x}\right)}{1+x^2}\,dx$
negative_passages.docid: 17852
negative_passages.text: $\int \frac{dx}{x\log(x)}$
negative_passages.docid: 148613
negative_passages.text: Integrate $\int_{0}^{1}{x^{-x}(1-x)^{x-1}\sin{\pi x}dx}$
negative_passages.docid: 31964
negative_passages.text: Evaluating $\int_0^{\infty}\frac{\ln(x^2+1)}{x^2+1}dx$
negative_passages.docid: 89499
negative_passages.text: Evaluating the integral $\int_0^{\frac{\pi}{2}}\log\left(\frac{1+a\cos(x)}{1-a\cos(x)}\right)\frac{1}{\cos(x)}dx$
negative_passages.docid: 5034
negative_passages.text: A closed form of $\int_0^1\frac{\ln\ln\left({1}/{x}\right)}{x^2-x+1}\mathrm dx$
negative_passages.docid: 68504
negative_passages.text: Compute $\int_0^1 \frac{\arcsin(x)}{x}dx$
negative_passages.docid: 137060
negative_passages.text: Evaluating $\int_0^{\tfrac{\pi}{4}}\ln(\cos x-\sin x)\ln(\cos x) dx - \int_0^{\tfrac{\pi}{4}}\ln(\cos x+\sin x)\ln(\sin x)dx=\frac{G\ln 2}{2}$
negative_passages.docid: 107119
negative_passages.text: A logarithmic integral $\int^1_0 \frac{\log\left(\frac{1+x}{1-x}\right)}{x\sqrt{1-x^2}}\,dx$