query: How to evaluate $\int_0^\infty \frac{1}{x^n+1} dx$
positive_passages.docid: 21240
positive_passages.text: Prove $\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$ using real analysis techniques only
negative_passages.docid: 146338
negative_passages.text: How to evaluate $\int\frac{1+x^4}{(1-x^4)^{3/2}}dx$?
negative_passages.docid: 31964
negative_passages.text: Evaluating $\int_0^{\infty}\frac{\ln(x^2+1)}{x^2+1}dx$
negative_passages.docid: 19514
negative_passages.text: $\int_0^{\infty } \frac{\log (x)}{e^x+1} \, dx = -\frac{1}{2} \log ^2(2)$ How to show?
negative_passages.docid: 65015
negative_passages.text: Computing $\lim_{n \to \infty} \sqrt[n]{ \int_{0}^{1} (1+x^n)^n dx}$
negative_passages.docid: 63863
negative_passages.text: Evaluate: $\sum_{n=1}^{\infty}\frac{1}{n k^n}$
negative_passages.docid: 137549
negative_passages.text: Given $\int_0^{\infty}e^{-x^2}dx = \frac{\sqrt{\pi}}{2}$, evaluate $\int_0^{\infty}e^{-a^2x^2-\frac{b^2}{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: 140638
negative_passages.text: Integrating $\int_0^{\infty} \frac{dx}{1+x^3}$ using residues.
negative_passages.docid: 84884
negative_passages.text: Need help with the integral $\int_{0}^\infty e^{-x^{2}}x^{2n+1}dx $
negative_passages.docid: 105860
negative_passages.text: Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$
negative_passages.docid: 38515
negative_passages.text: Integral of $\frac{1}{x^4+1}$
negative_passages.docid: 48233
negative_passages.text: Evaluating $\int_0^\infty \frac{dx}{1+x^4}$.
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: 100180
negative_passages.text: Evaluate the integral $\int_0^\infty \frac{dx}{\sqrt{(x^3+a^3)(x^3+b^3)}}$
negative_passages.docid: 107237
negative_passages.text: Evaluate $\lim_{n\rightarrow\infty} \int_0^1 f(x^n) dx$
negative_passages.docid: 33005
negative_passages.text: How to evaluate $\int_{0}^{+\infty}\exp(-ax^2-\frac b{x^2})\,dx$ for $a,b>0$