query: How to compute $\int_0^{\infty} \ln (1 + e^{-x})\, dx$ and $\int_0^{\infty} \ln (1 - e^{-x})\, dx$?
positive_passages.docid: 142516
positive_passages.text: Evaluating the integral, $\int_{0}^{\infty} \ln\left(1 - e^{-x}\right) \,\mathrm dx $
negative_passages.docid: 31964
negative_passages.text: Evaluating $\int_0^{\infty}\frac{\ln(x^2+1)}{x^2+1}dx$
negative_passages.docid: 102639
negative_passages.text: How to receive the result of the integral $ \int\frac{1}{x}dx$ is $\ln|x|$?
negative_passages.docid: 177
negative_passages.text: How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$
negative_passages.docid: 106812
negative_passages.text: Find $\int_{0}^{\infty} \frac{\ln(x)}{1+x^2}dx$
negative_passages.docid: 57686
negative_passages.text: Finding $ \int^1_0 \frac{\ln(1+x)}{x}dx$
negative_passages.docid: 74955
negative_passages.text: Simplify result of $\int_0^{\infty} \frac{1}{1+x^n}dx$
negative_passages.docid: 51284
negative_passages.text: $\int_{-\infty}^\infty \frac{e^{ax}}{1+e^x}dx$ with residue calculus
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: 34967
negative_passages.text: Compute $ \int_{0}^{ \infty }\frac{\ln xdx}{x^{2}+ax+b}$
negative_passages.docid: 11757
negative_passages.text: How can I compute the integral $\int_{0}^{\infty} \frac{dt}{1+t^4}$?
negative_passages.docid: 17996
negative_passages.text: Integral $\int_0^1 \frac{\ln(x+\sqrt{1-x^2})}{x}dx$
negative_passages.docid: 124445
negative_passages.text: Integral of the form $\int_{0}^{\infty}e^{-ax}e^{-x^{4}}dx$
negative_passages.docid: 140203
negative_passages.text: Find the value of $\int_{-\infty}^{\infty} \frac{e^{-x^2}}{1+x^2} dx$ .
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: 75423
negative_passages.text: Computing $\int_0^\infty\frac{1}{(1+x^{2015})(1+x^2)}$
negative_passages.docid: 84884
negative_passages.text: Need help with the integral $\int_{0}^\infty e^{-x^{2}}x^{2n+1}dx $