query: The special function $P(s)=\int^\infty_0 \frac{\ln(x)dx}{1+x^s}$
positive_passages.docid: 21857
positive_passages.text: Seeking methods to solve: $\int_0^\infty \frac{\ln(t)}{t^n + 1}\:dt$
negative_passages.docid: 78008
negative_passages.text: A conjectured closed form of $\int\limits_0^\infty\frac{x-1}{\sqrt{2^x-1}\ \ln\left(2^x-1\right)}dx$
negative_passages.docid: 68241
negative_passages.text: Integral $\int_0^1 \frac{\ln(1-x)\ln(1+x^2)}{x}dx$
negative_passages.docid: 35861
negative_passages.text: Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$
negative_passages.docid: 157725
negative_passages.text: does $\int _{1}^{\infty}\frac{p(x)}{e^x}$ converge?
negative_passages.docid: 10675
negative_passages.text: Proving that $\frac{1}{2\pi}\int_{0}^{2\pi}|f(re^{it})|^2dt=\sum_{n=0}^{\infty}|a_n|^2r^{2n}$
negative_passages.docid: 45440
negative_passages.text: $\sum_{n=2}^\infty \frac{1}{(\ln\, n)^2}$ c0nvergence
negative_passages.docid: 27195
negative_passages.text: Evaluating $\int_{0}^{1}\frac{1-x}{1+x}\frac{\mathrm dx}{\ln x}$
negative_passages.docid: 86843
negative_passages.text: Find the value of : $\lim_{n\to\infty}[(n+1)\int_{0}^{1}x^{n}\ln(1+x)dx]$.
negative_passages.docid: 148743
negative_passages.text: $\int_0^\infty \frac{1}{1+x^ 9} \, dx$
negative_passages.docid: 63956
negative_passages.text: Evaluate $\int_0^{\infty}\frac{\ln x}{x^a(x+1)}dx$ where $0<a<1$
negative_passages.docid: 133485
negative_passages.text: How to solve $\int_0^{\infty} \frac{\log(x+\frac{1}{x})}{1+x^2}dx$?
negative_passages.docid: 81831
negative_passages.text: Evaluate $\int_0^{\infty}\frac{\log x}{1+e^x}\,dx$
negative_passages.docid: 27705
negative_passages.text: Proof of $\int_{[0,\infty)}pt^{p-1}\mu(\{x:|f(x)|\geq t\})d\mu(t)=\int_{[0,\infty)}\mu(\{x:|f(x)|^p\geq s\})d\mu(s)$
negative_passages.docid: 112621
negative_passages.text: Finding $\int_{0}^{\infty} \frac{e^{3x}-e^x}{x(e^{3x}+1)(e^x+1)} dx$
negative_passages.docid: 19514
negative_passages.text: $\int_0^{\infty } \frac{\log (x)}{e^x+1} \, dx = -\frac{1}{2} \log ^2(2)$ How to show?
negative_passages.docid: 121736
negative_passages.text: An improper integral : $\int_{0}^\infty {\ln(a^2+x^2)\over{b^2+x^2}}dx$