query: Integral $\int_{-\infty}^{\infty} \frac{c(\theta)}{(1 + x^2)^\theta} dx $
positive_passages.docid: 151649
positive_passages.text: Exact Values of the integal $\int_0^\infty \frac{r^{n-1}}{(1+r^2)^{\frac{s}{2}}}\,dr$
negative_passages.docid: 13978
negative_passages.text: Calculating the integral $\int_0^\infty \frac{\cos x}{1+x^2}\, \mathrm{d}x$ without using complex analysis
negative_passages.docid: 61515
negative_passages.text: Evaluate $\int_0^{\infty} \frac{\log(x)dx}{x^2+a^2}$ using contour integration
negative_passages.docid: 114195
negative_passages.text: Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$
negative_passages.docid: 45622
negative_passages.text: Value of this definite integral $\int_{0}^{\infty} \frac{ \ln(x)}{x^2+2x+4} dx $
negative_passages.docid: 81258
negative_passages.text: Evaluation of $\int_{-\infty}^\infty \frac{\sin(at)}t\ dt$
negative_passages.docid: 109901
negative_passages.text: Computing $\int_0^\infty\frac1{(x+1)(x+2)\cdots(x+n)}\mathrm dx $
negative_passages.docid: 59667
negative_passages.text: Evaluating $\int_0^\infty\frac{\sin(x)}{x^2+1}\, dx$
negative_passages.docid: 6014
negative_passages.text: Evaluating $\int_{-\infty}^{\infty}\frac{\exp\left(-a x^2\right)}{x^2+b^2}dx$
negative_passages.docid: 29546
negative_passages.text: Residue integral: $\int_{- \infty}^{+ \infty} \frac{e^{ax}}{1+e^x} dx$ with $0 \lt a \lt 1$.
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: 30731
negative_passages.text: Integral ${\frac{1}{\pi^2}} \int_{0}^{\infty}\frac{{(\ln{x}})^2}{\sqrt{x}{(1-x)^2}} \mathrm d x$
negative_passages.docid: 124498
negative_passages.text: Show that $\int_{-\infty}^{\infty} \dfrac{x^2}{(x^2+1)^2(x^2+2x+2)} \ dx$ is convergent.
negative_passages.docid: 137549
negative_passages.text: Given $\int_0^{\infty}e^{-x^2}dx = \frac{\sqrt{\pi}}{2}$, evaluate $\int_0^{\infty}e^{-a^2x^2-\frac{b^2}{x^2}}dx $
negative_passages.docid: 21375
negative_passages.text: The integral $\int_0^\infty \dfrac{x \sin(x)}{x^2+1} dx$
negative_passages.docid: 123899
negative_passages.text: $\int_0^{+\infty}\frac{\sin(x)}{x^\alpha}dx=\frac{\Gamma(\alpha/2)\Gamma(1-\alpha/2)}{2\Gamma(\alpha)}$
negative_passages.docid: 108357
negative_passages.text: Integral $\int_0^\infty \log^2 x\frac{1+x^2}{1+x^4}dx=\frac{3 \pi^3}{16\sqrt 2}$