query: For which $\alpha$ does $\int_0^{\infty} \frac{\sin(x)}{x^{\alpha}}\,dx$ converge?
positive_passages.docid: 147662
positive_passages.text: For what values $s$ does $\int_{0}^{\infty} \frac{\sin x}{x^s}dx$ converge?
negative_passages.docid: 145335
negative_passages.text: Is $ \int_0^1{\frac{\sin x}{x}dx} $ convergent?
negative_passages.docid: 39798
negative_passages.text: Computing $\lim_{n \to \infty} \int_0^{n^2} e^{-x^2}n\sin\frac{x}{n}\,dx$?
negative_passages.docid: 109718
negative_passages.text: Does $\sum \limits_{n=1}^\infty\frac{\sin n}{n}(1+\frac{1}{2}+\cdots+\frac{1}{n})$ converge (absolutely)?
negative_passages.docid: 53831
negative_passages.text: Find a general solution for $\int_{0}^{\infty} \sin\left(x^n\right)\:dx$
negative_passages.docid: 21970
negative_passages.text: Convergence of the Power Series for $xu''+\sin(x)u=0$
negative_passages.docid: 53885
negative_passages.text: $\forall a > 0$ $\sum_{n=1}^{\infty} f(na)$ is convergent. Prove that $\int_{0}^{\infty}f(x) dx$ is convergent.
negative_passages.docid: 24056
negative_passages.text: Convergence of the improper integral $\int_{0}^{\pi/2}\tan^{p}(x) \; dx$
negative_passages.docid: 67340
negative_passages.text: Integrate $\int \frac{dx}{\sqrt{\sin^3x\sin(x+\alpha)}}$
negative_passages.docid: 122843
negative_passages.text: Finding $\int_0^\infty \frac{\cos(ax)-\cos(bx)}{x}dx$
negative_passages.docid: 134866
negative_passages.text: Does the integral $\int_{1}^{\infty} \sin(x\log x) \,\mathrm{d}x$ converge?
negative_passages.docid: 14050
negative_passages.text: Determining precisely where $\sum_{n=1}^\infty\frac{z^n}{n}$ converges?
negative_passages.docid: 72036
negative_passages.text: Closed form of $\int_0^\infty \sin(x)\sin\left(\frac{1}{x}\right)dx$?
negative_passages.docid: 4220
negative_passages.text: Does $\int_{0}^{\infty}\frac{dx}{1+(x\sin5x)^2}$ converge?
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: 147608
negative_passages.text: Cauchy principle value of $\int_{-\infty}^{\infty}\sin(x)/(x-a)dx$
negative_passages.docid: 23368
negative_passages.text: Does $\int_1^2\frac{\sin{x}}{\log{x}} \, dx$ converge?