query: How does k in $\int_{-\infty}^\infty ke^{\frac{-x^2}{2}} ~dx =1$ solve to $k = \frac{1}{\sqrt{2\pi}}$
positive_passages.docid: 4287
positive_passages.text: Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$
negative_passages.docid: 126046
negative_passages.text: solving the integral $ \int_0^\infty \dfrac{\sin xt}{x(x^2+1)} dx $
negative_passages.docid: 17986
negative_passages.text: Contour method to solve $\int^\infty_0\frac{\ln(1+x)}{1+x^2}\,dx$
negative_passages.docid: 28254
negative_passages.text: Why $\sum_{k=1}^{\infty} \frac{k}{2^k} = 2$?
negative_passages.docid: 21857
negative_passages.text: Seeking methods to solve: $\int_0^\infty \frac{\ln(t)}{t^n + 1}\:dt$
negative_passages.docid: 151127
negative_passages.text: Confirm that $\int_{0}^{\infty}t^{-1}\sin t dt=\pi/2$
negative_passages.docid: 8934
negative_passages.text: How do I solve this improper integral: $\int_{-\infty}^\infty e^{-x^2-x}dx$?
negative_passages.docid: 133955
negative_passages.text: Compute: $\sum_{k=1}^{\infty}\sum_{n=1}^{\infty} \frac{1}{k^2n+2nk+n^2k}$
negative_passages.docid: 24716
negative_passages.text: $\int_0^\infty\frac{\log x dx}{x^2-1}$ with a hint.
negative_passages.docid: 157255
negative_passages.text: Using residue theorem to integrate from $-\infty$ to $\infty$
negative_passages.docid: 143878
negative_passages.text: Solve: $\int x^3\sqrt{4-x^2}dx$
negative_passages.docid: 94869
negative_passages.text: Show that $ \int_{k}^{2} \frac{1}{f(y)} =1$
negative_passages.docid: 50844
negative_passages.text: How to compute $\int_0^{+\infty} \frac{dt}{1+t^4} = \frac{\pi}{2\sqrt 2}.$
negative_passages.docid: 107386
negative_passages.text: Compute $\lim_{n \to \infty} \int_0^{\frac{\pi}{2}} \sum_{k=1}^n (\sin{x})^kdx$
negative_passages.docid: 95426
negative_passages.text: How to compute $ \frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty \frac{e^{-{x^2}/{2}}}{1+e^{-(ax+b)}}\,\mathrm dx $ when $b \ne 0$
negative_passages.docid: 145183
negative_passages.text: finding $\int_0^\infty \dfrac{dx}{1+x^4}$ through complex analysis
negative_passages.docid: 765
negative_passages.text: $\int_0^\infty \frac{\log(x)}{x^2+\alpha^2}$ using residues