query: Determine if the integral converges $\intop_{1}^{2}\frac{\sin\left(x\right)}{\log\left(x\right)}$
positive_passages.docid: 23368
positive_passages.text: Does $\int_1^2\frac{\sin{x}}{\log{x}} \, dx$ converge?
negative_passages.docid: 81997
negative_passages.text: Evaluating $\lim_{n\to \infty}\frac1{2n}\log\left({2n \choose n}\right)$
negative_passages.docid: 94910
negative_passages.text: How does one show that $\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^x$ converges?
negative_passages.docid: 62443
negative_passages.text: Prove that $\sum_{n=1}^\infty \ln\left(\frac{n(n+2)}{(n+1)^2}\right)$ converges and find its sum
negative_passages.docid: 24716
negative_passages.text: $\int_0^\infty\frac{\log x dx}{x^2-1}$ with a hint.
negative_passages.docid: 117264
negative_passages.text: Prove that $\int_0^{\infty} \frac{\sin x}{x^p}\, dx$ converges for $0<p<2$
negative_passages.docid: 27347
negative_passages.text: Verify that $\left|\int_{\gamma} \exp(iz^2)dz\right| \leq \frac{\pi\big(1-\exp(-r^2)\big)}{4r}$ where $\gamma(t)=re^{it}$, for $0\leq t \leq \pi/4$.
negative_passages.docid: 58475
negative_passages.text: Does $\int_0^\infty |\cos(x^2)| \mathrm dx$ converge?
negative_passages.docid: 93610
negative_passages.text: What is $\int_0^1 \frac{\log \left(1-x^2\right) \sin ^{-1}(x)^2}{x^2} \, dx$?
negative_passages.docid: 6571
negative_passages.text: A Challenging Integral $\int_0^{\frac{\pi}{2}}\log \left( x^2+\log^2(\cos x)\right)dx$
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: 54730
negative_passages.text: For which $p$ does the series $\sum_{n=2}^{\infty} \frac{1}{(\log 1)^p+(\log 2)^p+\cdots +(\log n)^p}$ converge?
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: 27790
negative_passages.text: Evaluating $\int_0^{\large\frac{\pi}{4}} \log\left( \cos x\right) \, \mathrm{d}x $
negative_passages.docid: 105707
negative_passages.text: A proof of $\int_{0}^{1}\left( \frac{\ln t}{1-t}\right)^2\,\mathrm{d}t=\frac{\pi^2}{3}$
negative_passages.docid: 75459
negative_passages.text: study the convergence of $\sum_{n=1}^\infty \log \frac{n+1}{n}$
negative_passages.docid: 96505
negative_passages.text: Compute $\int_0^\infty \left(\frac{1}{x}\right)^{\ln(x)}\,\mathrm{d}x$