query: Integral of $\int_{-\infty}^\infty x^2e^{-\frac {(x-\mu)^2}{2\sigma^2}}dx$
positive_passages.docid: 143585
positive_passages.text: Solve the integral $\frac 1 {\sqrt {2 \pi t}}\int_{-\infty}^{\infty} x^2 e^{-\frac {x^2} {2t}}dx$
negative_passages.docid: 84413
negative_passages.text: Why is $\int_{-\infty}^\infty |g(x)|\,dx = \int_0^\infty \mu(\{x : |g(x)| \ge t\})\,dt$ true?
negative_passages.docid: 123694
negative_passages.text: How to compute the integral $\int_{0}^{\infty} \frac{x^{1/3}}{1+x^{2}} \ dx$
negative_passages.docid: 72039
negative_passages.text: Compute $\int_0^\infty\frac{\cos(xt)}{1+t^2}dt$
negative_passages.docid: 21375
negative_passages.text: The integral $\int_0^\infty \dfrac{x \sin(x)}{x^2+1} dx$
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: 104904
negative_passages.text: Calculating $\int_0^\infty \frac {\sin^2x}{x^2}dx$ using the Residue Theorem.
negative_passages.docid: 79908
negative_passages.text: Show $\int_0^\infty \frac{e^{-x}-e^{-xt}}{x}dx = \ln(t),$ for $t \gt 0$
negative_passages.docid: 142516
negative_passages.text: Evaluating the integral, $\int_{0}^{\infty} \ln\left(1 - e^{-x}\right) \,\mathrm dx $
negative_passages.docid: 140638
negative_passages.text: Integrating $\int_0^{\infty} \frac{dx}{1+x^3}$ using residues.
negative_passages.docid: 152339
negative_passages.text: Complex-valued Fourier integral: $ \int_{ - \infty }^{ + \infty } {\frac{{\cos (ax)}}{{{x^2} + 1}}{e^{ - ibx}}\,\mathrm dx} $
negative_passages.docid: 40537
negative_passages.text: How to prove $\int_0^\infty e^{-x^2}cos(2bx) dx = \frac{\sqrt{\pi}}{2} e^{-b^2}$
negative_passages.docid: 91196
negative_passages.text: Complex Integration of $\int_0^\infty e^{-ax}\cos(bx)\,dx$
negative_passages.docid: 56815
negative_passages.text: how to solve $\int_{-\infty}^\infty e^{-x^2-x{\tau}} \cdot x\ dx$?
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: 128572
negative_passages.text: How $\int_{-\infty}^{\infty}\frac{dx}{1+x^2}$ exists?
negative_passages.docid: 69978
negative_passages.text: Evaluating $\int_1^\infty \frac{1}{x(x^2+1)}\ dx$