query: Evaluating the integral $\int_{0}^{\infty} \frac{\cos ax}{1+x^2}dx$
positive_passages.docid: 152339
positive_passages.text: Complex-valued Fourier integral: $ \int_{ - \infty }^{ + \infty } {\frac{{\cos (ax)}}{{{x^2} + 1}}{e^{ - ibx}}\,\mathrm dx} $
negative_passages.docid: 21390
negative_passages.text: How to integrate $\int_0^{\infty} \frac{e^{ax} - e^{bx}}{(1 + e^{ax})(1+ e^{bx})}dx$ where $a,b > 0$.
negative_passages.docid: 59667
negative_passages.text: Evaluating $\int_0^\infty\frac{\sin(x)}{x^2+1}\, dx$
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: 70830
negative_passages.text: How to evaluate $\int_{0}^{\infty}\exp(-x^2-1/x^2)dx$?
negative_passages.docid: 31964
negative_passages.text: Evaluating $\int_0^{\infty}\frac{\ln(x^2+1)}{x^2+1}dx$
negative_passages.docid: 150890
negative_passages.text: Evaluating $\int_{\mathbb{R}}\frac{\exp(-x^2)}{1+x^2}\,\mathrm{d}x$
negative_passages.docid: 18672
negative_passages.text: Integrate $\int_{0}^{\pi}{\frac{x\cos{x}}{1+\sin^{2}{x}}dx}$
negative_passages.docid: 123694
negative_passages.text: How to compute the integral $\int_{0}^{\infty} \frac{x^{1/3}}{1+x^{2}} \ dx$
negative_passages.docid: 115598
negative_passages.text: Evaluating $\int_{0}^{1} dx\frac{\log(1+x)}{1 + x^2}$
negative_passages.docid: 90095
negative_passages.text: Integrate $\int_0^{\infty } \frac{\cos x}{x} dx$
negative_passages.docid: 128600
negative_passages.text: How to evaluate this integral$\int_{-\infty}^\infty\dfrac{\omega^\alpha e^{i\omega t}}{(\omega_0^2-\omega^2)^{2}+4(\zeta\omega_0\omega)^2}\,d\omega$
negative_passages.docid: 67263
negative_passages.text: Compute integral $\int_{-\infty}^\infty \frac{x^4}{1+x^8} \, dx$
negative_passages.docid: 141892
negative_passages.text: How to evaluate $\int_0^\infty \frac{1}{x^n+1} dx$
negative_passages.docid: 65407
negative_passages.text: Evaluating $\int\limits_0^\infty \frac{\log x} {(1+x^2)^2} dx$ with residue theory
negative_passages.docid: 115759
negative_passages.text: Evaluating this integral : $ \int \frac {1-7\cos^2x} {\sin^7x \cos^2x} dx $
negative_passages.docid: 69124
negative_passages.text: Integral $\int_{0}^{\infty}e^{-ax}\cos (bx)\operatorname d\!x$