query: Evaluate the $\int_0^\infty\frac{|\sin t|}{t}\;dt$
positive_passages.docid: 112951
positive_passages.text: Improper integral $\sin(x)/x $ converges absolutely, conditionaly or diverges?
negative_passages.docid: 86923
negative_passages.text: Evaluating the integral $\int_0^\infty \frac{x \sin rx }{a^2+x^2} dx$ using only real analysis
negative_passages.docid: 41738
negative_passages.text: Best way to integrate $ \int_0^\infty \frac{e^{-at} - e^{-bt}}{t} \text{d}t $
negative_passages.docid: 89602
negative_passages.text: $ \int_{0}^{ \infty} \int_{0}^{ \infty} \frac { e^{-(x+y)}}{x+y} dx dy $
negative_passages.docid: 35861
negative_passages.text: Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$
negative_passages.docid: 69978
negative_passages.text: Evaluating $\int_1^\infty \frac{1}{x(x^2+1)}\ dx$
negative_passages.docid: 57224
negative_passages.text: Compute $\int_0^\infty \frac{dx}{1+x^3}$
negative_passages.docid: 47572
negative_passages.text: Evaluate $ \sum_{n=1}^{\infty} \frac{\sin \ n}{ n } $ using the fourier series
negative_passages.docid: 84991
negative_passages.text: What contour should be used to evaluate $\int_0^\infty \frac{\sqrt{t}}{1+t^2} dt$
negative_passages.docid: 16049
negative_passages.text: Fourier transform of $\int_{-\infty}^{t}f(t)\, dt$
negative_passages.docid: 129892
negative_passages.text: show $\int_0^{\infty} \frac{x\sin ax}{x^2+t^2}dx = \frac{\pi}{2}e^{-at}$
negative_passages.docid: 76129
negative_passages.text: Evaluate $\int_0^\infty\frac{\sin(\varphi_1x)}x\frac{\sin\varphi_2x}x\cdots\frac{\sin\varphi_nx}x\frac{\sin(ax)}x\cos(a_1x)\cdots\cos(a_mx) \, dx$
negative_passages.docid: 4224
negative_passages.text: Evaluate limit of an integral: $\lim_{x\to \infty }\frac{1}{x}\int _0^x\:\frac{dt}{2+\cos t}$
negative_passages.docid: 24182
negative_passages.text: Evaluating $\int_{0}^{\infty}\frac{\sin^{2n+1}x}{x}\mathrm{d}x$
negative_passages.docid: 21375
negative_passages.text: The integral $\int_0^\infty \dfrac{x \sin(x)}{x^2+1} dx$
negative_passages.docid: 132000
negative_passages.text: Calculate $\int_0^\infty\frac{\sin x}xdx$ by integration of a suitable function along given paths
negative_passages.docid: 72039
negative_passages.text: Compute $\int_0^\infty\frac{\cos(xt)}{1+t^2}dt$