query: Find $\int_0^\infty \frac{\ln(x)}{1+x^2} \, dx$.
positive_passages.docid: 106812
positive_passages.text: Find $\int_{0}^{\infty} \frac{\ln(x)}{1+x^2}dx$
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: 144273
negative_passages.text: Find $\lim_{n\to\infty} \frac{1}{n} \int_0^\infty f(x) e^{-a_n x} dx$
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: 111636
negative_passages.text: Finding $\lim_{n\to\infty}\int_0^{\frac{1}{2^n}}(1+\cos(x))^n\,dx$
negative_passages.docid: 19631
negative_passages.text: Finding $\lim_{n\to \infty}\sqrt n \int_0^1 \frac{\,dx}{(1+x^2)^n}$
negative_passages.docid: 108554
negative_passages.text: Integrating $\int_0^\infty\frac{1}{1+x^6}dx$
negative_passages.docid: 102399
negative_passages.text: Computing $ \int_0^\infty \frac{\log x}{\exp x} \ dx $
negative_passages.docid: 59667
negative_passages.text: Evaluating $\int_0^\infty\frac{\sin(x)}{x^2+1}\, dx$
negative_passages.docid: 57686
negative_passages.text: Finding $ \int^1_0 \frac{\ln(1+x)}{x}dx$
negative_passages.docid: 128607
negative_passages.text: Integral $\int\frac{(\ln x)^{10}}{x}\,dx$
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: 126046
negative_passages.text: solving the integral $ \int_0^\infty \dfrac{\sin xt}{x(x^2+1)} dx $
negative_passages.docid: 89602
negative_passages.text: $ \int_{0}^{ \infty} \int_{0}^{ \infty} \frac { e^{-(x+y)}}{x+y} dx dy $
negative_passages.docid: 102932
negative_passages.text: Integral $\int_0^\infty \frac{\arctan(x) dx}{x(1+x^2)}$?
negative_passages.docid: 146349
negative_passages.text: $\int_0^\infty \frac{\ln\left(1+x-\sqrt{2x}\right)}{1+x^2}\,dx$
negative_passages.docid: 49074
negative_passages.text: Compute $\int\limits_{-\infty}^{\infty}\frac{1}{(1+x^2)^{n+1}}dx$ via residue calculus.