query: Cauchy's Principal Value of $\int_{-\infty}^{\infty} \sin(x)/(a-x)dx$
positive_passages.docid: 147608
positive_passages.text: Cauchy principle value of $\int_{-\infty}^{\infty}\sin(x)/(x-a)dx$
negative_passages.docid: 77322
negative_passages.text: Uniform continuity of $\sin(x\sin x )$ for all $x\in (0,\infty)$
negative_passages.docid: 105494
negative_passages.text: Gaussian-like integral : $\int_0^{\infty} e^{-x^2} \cos( a x) \ \mathrm{d}x$
negative_passages.docid: 122843
negative_passages.text: Finding $\int_0^\infty \frac{\cos(ax)-\cos(bx)}{x}dx$
negative_passages.docid: 144039
negative_passages.text: Computing $ \int_0^{\infty} \frac{ \sqrt [3] {x+1}-\sqrt [3] {x}}{\sqrt{x}} \mathrm 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: 89421
negative_passages.text: Does $\int_{1}^{\infty} g(x)\ dx$ imply $\lim\limits_{x\to \infty}g(x)=0$?
negative_passages.docid: 152648
negative_passages.text: Is the integral $\int_1^\infty\frac{x^{-a} - x^{-b}}{\log(x)}\,dx$ convergent?
negative_passages.docid: 69124
negative_passages.text: Integral $\int_{0}^{\infty}e^{-ax}\cos (bx)\operatorname d\!x$
negative_passages.docid: 145183
negative_passages.text: finding $\int_0^\infty \dfrac{dx}{1+x^4}$ through complex analysis
negative_passages.docid: 68866
negative_passages.text: Is $\int_{-\infty}^{\infty} \sin x \, \mathrm{dx}$ divergent or convergent?
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: 70845
negative_passages.text: Contour method to show that $\int_0^\infty\frac{x-\sin x}{x^3} \, dx=\frac\pi4$
negative_passages.docid: 9926
negative_passages.text: About the relation between $\int_{0}^{\infty}\frac{\cosh((\alpha-\beta)x)}{(\cosh(x))^{\alpha+\beta }} \,dx$ and $B(\alpha,\beta)$
negative_passages.docid: 158147
negative_passages.text: Calculating $\int_{-\infty}^{\infty}\frac{\sin(ax)}{x}\, dx$ using complex analysis
negative_passages.docid: 24182
negative_passages.text: Evaluating $\int_{0}^{\infty}\frac{\sin^{2n+1}x}{x}\mathrm{d}x$
negative_passages.docid: 102932
negative_passages.text: Integral $\int_0^\infty \frac{\arctan(x) dx}{x(1+x^2)}$?