query: Compute $\int\frac{du}{\sqrt{a^2-u^2}}$
positive_passages.docid: 154035
positive_passages.text: Why is arcsine the odd one out?
negative_passages.docid: 77721
negative_passages.text: Is it possible to compute $\int_1^{+ \infty} \frac{dx}{x^2(1+e^x)}$?
negative_passages.docid: 39629
negative_passages.text: Indefinite integration of $\int \frac{1}{1+\sqrt{x^2+2x+2}}dx$
negative_passages.docid: 96414
negative_passages.text: Using residues to evaluate the integral $\int_{-\pi}^{\pi} \frac{\cos(n\theta)}{1-2a\cos(\theta)+a^2}d\theta$, $|a|<1$
negative_passages.docid: 53519
negative_passages.text: Finding $\int_0^1{\frac{x^4(1-x)^4}{1+x^2}}dx$
negative_passages.docid: 146338
negative_passages.text: How to evaluate $\int\frac{1+x^4}{(1-x^4)^{3/2}}dx$?
negative_passages.docid: 144811
negative_passages.text: Calculate $\int_0^{2\pi} \frac{1}{2+\sin(x)} \ dx$
negative_passages.docid: 102156
negative_passages.text: Integral of $\int_0^{\pi/2} \frac {\sqrt{\sin x}}{\sqrt {\sin x} + \sqrt {\cos x}}$dx
negative_passages.docid: 154491
negative_passages.text: Evaluate $\int \frac{\sqrt{x^2-1}}{x} \mathrm{d}x$
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: 84765
negative_passages.text: Evaluating $\int_{-\infty}^{\infty}\frac{1}{(x^2+b^2)^2}dx$
negative_passages.docid: 62450
negative_passages.text: Computing $ \int_0^{2\pi} \frac{1}{a^2\cos^2 t+b^2 \sin^2 t} dt \;; a,b>0$.
negative_passages.docid: 140122
negative_passages.text: Integral: $\int_0^1\frac{\mathrm{Li}_2(x^2)}{\sqrt{1-x^2}}dx$
negative_passages.docid: 105260
negative_passages.text: How to integrate $\int\sqrt{x^2+1}dx$
negative_passages.docid: 147759
negative_passages.text: Integral $ \dfrac { \int_0^{\pi/2} (\sin x)^{\sqrt 2 + 1} dx} { \int_0^{\pi/2} (\sin x)^{\sqrt 2 - 1} dx} $
negative_passages.docid: 104094
negative_passages.text: Integral of $\frac{1}{(1+x^2)^2}$
negative_passages.docid: 45212
negative_passages.text: Integrals involving reciprocal square root of a quartic