query: Integral of $x^{-x}$ from $0$ to infinity $=$ $2$?
positive_passages.docid: 45205
positive_passages.text: Showing that $\int_0^\infty x^{-x} \mathrm{d}x \leq 2$.
negative_passages.docid: 47793
negative_passages.text: Integral $\int_0^1\sqrt{1-x^4}dx$
negative_passages.docid: 85081
negative_passages.text: $\int_{0}^{\infty} \frac{\cos x - e^{-x}}{x} \mathrm dx$ Evaluate Integral
negative_passages.docid: 76400
negative_passages.text: Finding $\int^{\infty}_{0}\frac{\ln^2(x)}{(1-x^2)^2} dx$
negative_passages.docid: 42758
negative_passages.text: How to find $ \int_0^\infty \dfrac x{1+e^x}\ dx$
negative_passages.docid: 79633
negative_passages.text: Calculating the integral $\int_{-\infty}^{\infty} x\sin(x)/(x^2+1)^2 dx$
negative_passages.docid: 74454
negative_passages.text: Sophomore's dream: $\int_0^{1} x^{-x} \; dx = \sum_{n=1}^\infty n^{-n}$
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: 96191
negative_passages.text: Integral $\int_0^{\infty} \sin(x^2)/x^2\,dx$
negative_passages.docid: 98710
negative_passages.text: Finding $\int_0^{\infty}xe^{-\lambda x} \, dx$
negative_passages.docid: 35861
negative_passages.text: Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$
negative_passages.docid: 54735
negative_passages.text: What is the closed form of $\int e^{x^2} \, dx$?
negative_passages.docid: 4693
negative_passages.text: what is the$ \int \sin (x^2) \, dx$?
negative_passages.docid: 115375
negative_passages.text: Indefinite integral of $e^{x^n}$
negative_passages.docid: 3704
negative_passages.text: Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$?
negative_passages.docid: 21375
negative_passages.text: The integral $\int_0^\infty \dfrac{x \sin(x)}{x^2+1} dx$
negative_passages.docid: 104138
negative_passages.text: How to integrate $\int\limits_0^\infty e^{-a x^2}\cos(b x) dx$ where $a>0$