query: How to find the value of $\int_0^1 \frac{x-1}{\log x}\,dx$?
positive_passages.docid: 46310
positive_passages.text: Showing that $ \int_{0}^{1} \frac{x-1}{\ln(x)} \mathrm dx=\ln2 $
negative_passages.docid: 118324
negative_passages.text: Other challenging logarithmic integral $\int_0^1 \frac{\log^2(x)\log(1-x)\log(1+x)}{x}dx$
negative_passages.docid: 125523
negative_passages.text: How to find $\int_{0}^{\pi/2} \log ({1+\cos x}) dx$ using real-variable methods?
negative_passages.docid: 92637
negative_passages.text: Evaluating $\int \frac{\operatorname dx}{x\log x}$
negative_passages.docid: 24974
negative_passages.text: Closed form for $\int_0^1\log\log\left(\frac{1}{x}+\sqrt{\frac{1}{x^2}-1}\right)\mathrm dx$
negative_passages.docid: 144942
negative_passages.text: Obtain the value of $\int_0^1f(x) \ dx$, where $f(x) = \begin{cases} \frac {1}{n}, & \frac{1}{n+1}<x\le\frac{1}{n}\\ 0, & x=0 \end{cases}$
negative_passages.docid: 17996
negative_passages.text: Integral $\int_0^1 \frac{\ln(x+\sqrt{1-x^2})}{x}dx$
negative_passages.docid: 64743
negative_passages.text: How do I evaluate the integral $\int \frac{1}{x^3 -1}dx$
negative_passages.docid: 68241
negative_passages.text: Integral $\int_0^1 \frac{\ln(1-x)\ln(1+x^2)}{x}dx$
negative_passages.docid: 8289
negative_passages.text: Hints on calculating the integral $\int_0^1\frac{x^{19}-1}{\ln x}\,dx$
negative_passages.docid: 81914
negative_passages.text: Integrating $\int_0^1 \frac {\log(1-x)\log^2(1+x)}x \mathrm{d}x$
negative_passages.docid: 31660
negative_passages.text: Integral $\int_{0}^{1}\left\{\frac{1}{x}\right\}\left\{\frac{1}{1-x}\right\}\left\{1-\frac{1}{x}\right\} d x=?$
negative_passages.docid: 65982
negative_passages.text: Evaluate the improper integral $ \int_0^1 \frac{\ln(1+x)}{x}\,dx $
negative_passages.docid: 68639
negative_passages.text: given $I_{n}=\int^1_{0}x^n\sqrt{1-x^2}dx$, then finding value of $ \frac{I_{n}}{I_{n-2}}$
negative_passages.docid: 85949
negative_passages.text: Integral involving logarithm: $\int_0^\infty \frac{ \ln x}{(x+a)(x+b)} dx$
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: 45622
negative_passages.text: Value of this definite integral $\int_{0}^{\infty} \frac{ \ln(x)}{x^2+2x+4} dx $