query: Evaluate $\int \limits_{-\infty}^{\infty}\frac{1}{1+x^4}dx$ using complex analysis
positive_passages.docid: 145183
positive_passages.text: finding $\int_0^\infty \dfrac{dx}{1+x^4}$ through complex analysis
negative_passages.docid: 101536
negative_passages.text: Difficult limit evaluation: $\lim_{x\to\infty}(\sqrt{x^2+4x} - x)$
negative_passages.docid: 11757
negative_passages.text: How can I compute the integral $\int_{0}^{\infty} \frac{dt}{1+t^4}$?
negative_passages.docid: 129913
negative_passages.text: Evaluate: $I=\int\limits_{0}^{\frac{\pi}{2}}\ln\frac{(1+\sin x)^{1+\cos x}}{1+\cos x}dx$
negative_passages.docid: 4224
negative_passages.text: Evaluate limit of an integral: $\lim_{x\to \infty }\frac{1}{x}\int _0^x\:\frac{dt}{2+\cos t}$
negative_passages.docid: 109606
negative_passages.text: Detail in the use of the Residue Theorem for $\int\limits_{-\infty}^{\infty}\frac{\cos(2x)-1}{x^2}dx$
negative_passages.docid: 115420
negative_passages.text: Evaluate $\sum_{n=1}^{\infty} \frac{n}{n^4+n^2+1}$
negative_passages.docid: 67263
negative_passages.text: Compute integral $\int_{-\infty}^\infty \frac{x^4}{1+x^8} \, dx$
negative_passages.docid: 27002
negative_passages.text: Evaluating $\int\limits_0^{\pi} \frac{dx}{1+2\sin^2x}$
negative_passages.docid: 58646
negative_passages.text: Are there any ways to evaluate $\int^\infty_0\frac{\sin x}{x}dx$ without using double integral?
negative_passages.docid: 84765
negative_passages.text: Evaluating $\int_{-\infty}^{\infty}\frac{1}{(x^2+b^2)^2}dx$
negative_passages.docid: 76400
negative_passages.text: Finding $\int^{\infty}_{0}\frac{\ln^2(x)}{(1-x^2)^2} dx$
negative_passages.docid: 154286
negative_passages.text: Evaluating $\lim_{n \to \infty} (1 + 1/n)^{n}$
negative_passages.docid: 122301
negative_passages.text: Evaluating and proving $\lim\limits_{x\to\infty}\frac{\sin x}x$
negative_passages.docid: 151149
negative_passages.text: $\lim_{n \to \infty} n \int_{1}^{\infty} \frac{dx}{1+x^n}$, solution critique needed
negative_passages.docid: 84034
negative_passages.text: Evaluate $\int_{-\infty}^{\infty} \chi_{[0,1]}(x-y) \chi_{[0,1]}(y) \, \mathrm{d}y$
negative_passages.docid: 105860
negative_passages.text: Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$