query: Evaluating the integral:$\int_0^\infty x\left(\log\left(\frac1{x^2}\right)\right)^n dx$
positive_passages.docid: 155981
positive_passages.text: Evaluate an proper integral:$\int_0^\infty x\left(\log\left(\frac1{x^2}\right)\right)^n dx$
negative_passages.docid: 66852
negative_passages.text: Integral $ \int_{-\infty}^{\infty}\frac{x^{2}}{\cosh\left(x\right)}\,{\rm d}x $
negative_passages.docid: 106812
negative_passages.text: Find $\int_{0}^{\infty} \frac{\ln(x)}{1+x^2}dx$
negative_passages.docid: 138174
negative_passages.text: Integral $\int_0^1 \frac{x\ln\left(\frac{1+x}{1-x}\right)}{\left(\pi^2+\ln^2\left(\frac{1+x}{1-x}\right)\right)^2}dx$
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: 96505
negative_passages.text: Compute $\int_0^\infty \left(\frac{1}{x}\right)^{\ln(x)}\,\mathrm{d}x$
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: 67837
negative_passages.text: Evaluation of $\int_{0}^{1}\frac{x\ln (x)}{\sqrt{1-x^2}}dx$
negative_passages.docid: 93071
negative_passages.text: Is there a way to calculate the improper integral $\int_0^\infty \big(\frac{\ln x}{x - 1}\big)^2 dx$?
negative_passages.docid: 828
negative_passages.text: Computing the integral of $\log(\sin x)$
negative_passages.docid: 142516
negative_passages.text: Evaluating the integral, $\int_{0}^{\infty} \ln\left(1 - e^{-x}\right) \,\mathrm dx $
negative_passages.docid: 46898
negative_passages.text: Fast calculation for $\int_{0}^{\infty}\frac{\log x}{x^2+1}dx=0$
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: 99753
negative_passages.text: How to prove $\int_0^1\frac{1-x}{(\ln x)(1+x)}\ dx=\ln\left(\frac2{\pi}\right)$?
negative_passages.docid: 40881
negative_passages.text: Evaluate $\int_{0}^{+\infty }{\left( \frac{x}{{{\text{e}}^{x}}-{{\text{e}}^{-x}}}-\frac{1}{2} \right)\frac{1}{{{x}^{2}}}\text{d}x}$
negative_passages.docid: 89499
negative_passages.text: Evaluating the integral $\int_0^{\frac{\pi}{2}}\log\left(\frac{1+a\cos(x)}{1-a\cos(x)}\right)\frac{1}{\cos(x)}dx$
negative_passages.docid: 155919
negative_passages.text: Integral $\small \int_0^\infty \frac{(\pi x - 2\log{x})^3}{\left(\log^2{x} + \frac{\pi^2}{4}\right)(1+x^2)^2} \text{d}x$