query: How to evaluate the integral $\int_0^\infty \frac{1}{(1+x^2)(1+x^\alpha)} \mathbb dx$?
positive_passages.docid: 89956
positive_passages.text: Is the integral $\int_0^\infty \frac{\mathrm{d} x}{(1+x^2)(1+x^a)}$ equal for all $a \neq 0$?
negative_passages.docid: 106812
negative_passages.text: Find $\int_{0}^{\infty} \frac{\ln(x)}{1+x^2}dx$
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: 140122
negative_passages.text: Integral: $\int_0^1\frac{\mathrm{Li}_2(x^2)}{\sqrt{1-x^2}}dx$
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: 48233
negative_passages.text: Evaluating $\int_0^\infty \frac{dx}{1+x^4}$.
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: 102932
negative_passages.text: Integral $\int_0^\infty \frac{\arctan(x) dx}{x(1+x^2)}$?
negative_passages.docid: 145183
negative_passages.text: finding $\int_0^\infty \dfrac{dx}{1+x^4}$ through complex analysis
negative_passages.docid: 119410
negative_passages.text: Solution of $\int_0^\infty\frac{\ln(1+{x^2})}{1+{x^2}}$
negative_passages.docid: 42758
negative_passages.text: How to find $ \int_0^\infty \dfrac x{1+e^x}\ 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: 150809
negative_passages.text: Compute $ \int_0^1\frac{\ln^2(1+x)}{1+x^2}\, dx$
negative_passages.docid: 83325
negative_passages.text: Integral of $\frac{\sqrt{x^2+1}}{x}$
negative_passages.docid: 38515
negative_passages.text: Integral of $\frac{1}{x^4+1}$
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: 123899
negative_passages.text: $\int_0^{+\infty}\frac{\sin(x)}{x^\alpha}dx=\frac{\Gamma(\alpha/2)\Gamma(1-\alpha/2)}{2\Gamma(\alpha)}$