query: Evaluate $\int_{0}^{\infty} \frac{e^{ax}-e^{bx}}{(1+e^{ax})(1+e^{bx})} dx$
positive_passages.docid: 21390
positive_passages.text: How to integrate $\int_0^{\infty} \frac{e^{ax} - e^{bx}}{(1 + e^{ax})(1+ e^{bx})}dx$ where $a,b > 0$.
negative_passages.docid: 84034
negative_passages.text: Evaluate $\int_{-\infty}^{\infty} \chi_{[0,1]}(x-y) \chi_{[0,1]}(y) \, \mathrm{d}y$
negative_passages.docid: 41738
negative_passages.text: Best way to integrate $ \int_0^\infty \frac{e^{-at} - e^{-bt}}{t} \text{d}t $
negative_passages.docid: 53830
negative_passages.text: Evaluate $ \int_{0}^{1} \ln(x)\ln(1-x)\,dx $
negative_passages.docid: 81621
negative_passages.text: How to evaluate the integral $\int_{0}^{\infty}\frac{\cos {(ax)}-\cos{(b x)}}{x^2 }dx$?
negative_passages.docid: 15569
negative_passages.text: Integral of the form $\int_0^\infty \exp{\left(-\frac{(a+bx)^2}{x}\right)}\frac{dx}{\sqrt{x^3}}$
negative_passages.docid: 76129
negative_passages.text: Evaluate $\int_0^\infty\frac{\sin(\varphi_1x)}x\frac{\sin\varphi_2x}x\cdots\frac{\sin\varphi_nx}x\frac{\sin(ax)}x\cos(a_1x)\cdots\cos(a_mx) \, dx$
negative_passages.docid: 115598
negative_passages.text: Evaluating $\int_{0}^{1} dx\frac{\log(1+x)}{1 + x^2}$
negative_passages.docid: 109385
negative_passages.text: Evaluating the integral $\int_{-\ln 2}^{\ln 2} e^{-x}(\sin x+x)^{1/3}dx$
negative_passages.docid: 69124
negative_passages.text: Integral $\int_{0}^{\infty}e^{-ax}\cos (bx)\operatorname d\!x$
negative_passages.docid: 68319
negative_passages.text: How can I evaluate $\int_{-\infty}^{\infty} e^{-x^2} dx$ without using polar coordinates
negative_passages.docid: 65982
negative_passages.text: Evaluate the improper integral $ \int_0^1 \frac{\ln(1+x)}{x}\,dx $
negative_passages.docid: 29546
negative_passages.text: Residue integral: $\int_{- \infty}^{+ \infty} \frac{e^{ax}}{1+e^x} dx$ with $0 \lt a \lt 1$.
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: 6014
negative_passages.text: Evaluating $\int_{-\infty}^{\infty}\frac{\exp\left(-a x^2\right)}{x^2+b^2}dx$
negative_passages.docid: 111775
negative_passages.text: $\int_{-\infty}^{+\infty} e^{-x^2} dx$ with complex analysis
negative_passages.docid: 51284
negative_passages.text: $\int_{-\infty}^\infty \frac{e^{ax}}{1+e^x}dx$ with residue calculus