query: If $1 = c . \int_{- \infty}^{\infty} e^{-x^2}dx$ , then what is c?
positive_passages.docid: 4287
positive_passages.text: Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$
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: 121736
negative_passages.text: An improper integral : $\int_{0}^\infty {\ln(a^2+x^2)\over{b^2+x^2}}dx$
negative_passages.docid: 91680
negative_passages.text: Does $\lim_{n\to \infty} \int^{\infty}_{-\infty} f_n(x) dx\, = \int^{\infty}_{-\infty} f(x)\,dx\,$?
negative_passages.docid: 133485
negative_passages.text: How to solve $\int_0^{\infty} \frac{\log(x+\frac{1}{x})}{1+x^2}dx$?
negative_passages.docid: 84765
negative_passages.text: Evaluating $\int_{-\infty}^{\infty}\frac{1}{(x^2+b^2)^2}dx$
negative_passages.docid: 30829
negative_passages.text: A question in Complex Analysis $\int_0^{2\pi}\log(1-2r\cos x +r^2)\,dx$
negative_passages.docid: 79361
negative_passages.text: What is the integral of 1/x?
negative_passages.docid: 122843
negative_passages.text: Finding $\int_0^\infty \frac{\cos(ax)-\cos(bx)}{x}dx$
negative_passages.docid: 12217
negative_passages.text: What is so special about $\alpha=-1$ in the integral of $x^\alpha$?
negative_passages.docid: 66902
negative_passages.text: Prove that $\int_{-\infty}^{\infty} \frac{e^{2x}-e^x}{x (1+e^{2x})(1+e^{x})}\mathrm{d}x=\log 2$
negative_passages.docid: 100194
negative_passages.text: Calculating $ \int _{0} ^{\infty} \frac{x^{3}}{e^{x}-1}\;dx$
negative_passages.docid: 76400
negative_passages.text: Finding $\int^{\infty}_{0}\frac{\ln^2(x)}{(1-x^2)^2} dx$
negative_passages.docid: 10806
negative_passages.text: Find the value of $\int_{-\infty}^\infty \int_{-\infty}^\infty e^{-(x^2+xy+y^2)} \, dx\,dy$
negative_passages.docid: 128572
negative_passages.text: How $\int_{-\infty}^{\infty}\frac{dx}{1+x^2}$ exists?
negative_passages.docid: 100711
negative_passages.text: $\int_{-\infty}^{\infty}e^{-zt^2 + 2wt} \ dt = e^{w^2 / z} \sqrt{\frac{\pi}{z}}$ for $z,w \in \mathbb{C}, Re(z) > 0$
negative_passages.docid: 140260
negative_passages.text: Is $\int \frac{1}{2x} \, dx $ equal to $\frac{\ln|2x|}{2}+ C$ or $\frac{\ln|x|}{2}+ C$