query: How to evaluate $ \int_{-\infty}^{+\infty} \frac{x\sin(x)}{x^2 +1} \,dx $
positive_passages.docid: 138355
positive_passages.text: Improper rational/trig integral comes out to $\pi/e$
negative_passages.docid: 119669
negative_passages.text: Evaluate $\int \frac{1}{\sin x\cos x} dx $
negative_passages.docid: 70830
negative_passages.text: How to evaluate $\int_{0}^{\infty}\exp(-x^2-1/x^2)dx$?
negative_passages.docid: 153867
negative_passages.text: Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$
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: 145590
negative_passages.text: Compute the integral $\int\frac{dx}{(x^2-x+1)\sqrt{x^2+x+1}}$
negative_passages.docid: 71982
negative_passages.text: Evaluating this integral $ \small\int \frac {x^2 dx} {(x\sin x+\cos x)^2} $
negative_passages.docid: 104904
negative_passages.text: Calculating $\int_0^\infty \frac {\sin^2x}{x^2}dx$ using the Residue Theorem.
negative_passages.docid: 29425
negative_passages.text: $\int_{0}^{\infty}\frac{\sin^{2n+1}(x)}{x} \mathrm {d}x$ Evaluate Integral
negative_passages.docid: 114195
negative_passages.text: Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$
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: 57463
negative_passages.text: Evaluate the integral using the theory of residues: $\int_{-\infty}^{\infty} \frac{dx}{(x^2+1)^2(x^2+16)}$
negative_passages.docid: 132124
negative_passages.text: $\int_{0}^{\infty}\frac{x}{x^3+1}dx$ =?
negative_passages.docid: 100401
negative_passages.text: Evaluate $\int \frac{1}{(x^2+1)^2}dx$
negative_passages.docid: 149341
negative_passages.text: Help me evaluate $\int_0^1 \frac{\log(x+1)}{1+x^2} dx$
negative_passages.docid: 129913
negative_passages.text: Evaluate: $I=\int\limits_{0}^{\frac{\pi}{2}}\ln\frac{(1+\sin x)^{1+\cos x}}{1+\cos x}dx$
negative_passages.docid: 117587
negative_passages.text: $\int_{0}^{1}\frac{\sin^{-1}\sqrt x}{x^2-x+1}dx$