query: Use the substitution $u = \frac{1}{x}$ to show that $\int_{0}^{\infty} \frac{\ln(x)}{1+x^2} dx = 0$
positive_passages.docid: 35861
positive_passages.text: Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$
negative_passages.docid: 79908
negative_passages.text: Show $\int_0^\infty \frac{e^{-x}-e^{-xt}}{x}dx = \ln(t),$ for $t \gt 0$
negative_passages.docid: 148743
negative_passages.text: $\int_0^\infty \frac{1}{1+x^ 9} \, dx$
negative_passages.docid: 114673
negative_passages.text: Proving the convergence of $\sum_{n=2}^{\infty} \frac{1}{n (\ln n)^2}$
negative_passages.docid: 68241
negative_passages.text: Integral $\int_0^1 \frac{\ln(1-x)\ln(1+x^2)}{x}dx$
negative_passages.docid: 40310
negative_passages.text: How to integrate $\frac{1}{\sqrt{1+x^2}}$ using substitution?
negative_passages.docid: 63956
negative_passages.text: Evaluate $\int_0^{\infty}\frac{\ln x}{x^a(x+1)}dx$ where $0<a<1$
negative_passages.docid: 41515
negative_passages.text: fine the limit : $\lim_{ n \to \infty }\frac{1}{n}\int_{0}^{n}{ \frac{x\ln(1+\frac{x}{n})}{1+x}}=?$
negative_passages.docid: 109416
negative_passages.text: How to calculate $\int_0^1 \frac{\ln(1-x)}{x} dx$?
negative_passages.docid: 98836
negative_passages.text: Showing $\int_x^{x+1}f(t)\,dt \xrightarrow{x\to\infty}0$ for $f\in L^2 (\mathbb{R})$
negative_passages.docid: 108554
negative_passages.text: Integrating $\int_0^\infty\frac{1}{1+x^6}dx$
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: 115992
negative_passages.text: Integrating $\frac{\log(1+x)}{1+x^2}$
negative_passages.docid: 8289
negative_passages.text: Hints on calculating the integral $\int_0^1\frac{x^{19}-1}{\ln x}\,dx$
negative_passages.docid: 23087
negative_passages.text: Evaluate $\int_0^\infty \frac{(\log x)^2}{1+x^2} dx$ using complex analysis
negative_passages.docid: 85618
negative_passages.text: Integral of $\frac{x^\alpha}{(1 + x^2)^2}$ from 0 to $\infty$ using contour integration for $-1 < \alpha <3$
negative_passages.docid: 128572
negative_passages.text: How $\int_{-\infty}^{\infty}\frac{dx}{1+x^2}$ exists?