query: Find $\int_0^\infty\frac{x\log x}{(1+x^2)^2}dx$
positive_passages.docid: 147108
positive_passages.text: Prove that $\int_0^\infty \frac{x\,\log x}{(1+x^2)^2} = 0$
negative_passages.docid: 75267
negative_passages.text: integrate the following function: $\int_{0}^{\infty} \frac{\log{x}}{x^{2}+a^{2}} \ dx$
negative_passages.docid: 109121
negative_passages.text: How to find integral of $\int_0^\infty \frac{\ln ^2z} {1+z^2}\mathrm{d}z$?
negative_passages.docid: 119410
negative_passages.text: Solution of $\int_0^\infty\frac{\ln(1+{x^2})}{1+{x^2}}$
negative_passages.docid: 133160
negative_passages.text: Closed form for $\int_0^\infty\frac{1}{(1+x^2)^s}\,dx$ when $s\in (0.5,\infty)\setminus\mathbb{N}$
negative_passages.docid: 17852
negative_passages.text: $\int \frac{dx}{x\log(x)}$
negative_passages.docid: 108554
negative_passages.text: Integrating $\int_0^\infty\frac{1}{1+x^6}dx$
negative_passages.docid: 75423
negative_passages.text: Computing $\int_0^\infty\frac{1}{(1+x^{2015})(1+x^2)}$
negative_passages.docid: 765
negative_passages.text: $\int_0^\infty \frac{\log(x)}{x^2+\alpha^2}$ using residues
negative_passages.docid: 128572
negative_passages.text: How $\int_{-\infty}^{\infty}\frac{dx}{1+x^2}$ exists?
negative_passages.docid: 42758
negative_passages.text: How to find $ \int_0^\infty \dfrac x{1+e^x}\ dx$
negative_passages.docid: 16775
negative_passages.text: Showing that $\int_{0}^{\infty} \frac{dx}{1 + x^2} = 2 \int_0^1 \frac{dx}{1 + x^2}$
negative_passages.docid: 10806
negative_passages.text: Find the value of $\int_{-\infty}^\infty \int_{-\infty}^\infty e^{-(x^2+xy+y^2)} \, dx\,dy$
negative_passages.docid: 104094
negative_passages.text: Integral of $\frac{1}{(1+x^2)^2}$
negative_passages.docid: 57686
negative_passages.text: Finding $ \int^1_0 \frac{\ln(1+x)}{x}dx$
negative_passages.docid: 66902
negative_passages.text: Prove that $\int_{-\infty}^{\infty} \frac{e^{2x}-e^x}{x (1+e^{2x})(1+e^{x})}\mathrm{d}x=\log 2$
negative_passages.docid: 152648
negative_passages.text: Is the integral $\int_1^\infty\frac{x^{-a} - x^{-b}}{\log(x)}\,dx$ convergent?