query: How do I integrate $\sqrt{a^2 - x^2}$?
positive_passages.docid: 146084
positive_passages.text: Different methods of evaluating $\int\sqrt{a^2-x^2}dx$:
negative_passages.docid: 29680
negative_passages.text: How to determine $\int x^2 e^{-x^2}\mathrm dx$?
negative_passages.docid: 125069
negative_passages.text: Help with $\int \frac 1{\sqrt{a^2 - x^2}} \mathrm dx$
negative_passages.docid: 84683
negative_passages.text: integrate $dx/(a^2 \cos^2x+b^2 \sin^2x)^2$
negative_passages.docid: 135447
negative_passages.text: Compute the integral $\int_0^{\frac\pi2}\frac{\mathrm d \theta}{\sqrt{\sin \theta}}$
negative_passages.docid: 81533
negative_passages.text: Integrating $\int_1^2 \int_0^ \sqrt{2x-x^2} \frac{1}{((x^2+y^2)^2} dydx $ in polar coordinates
negative_passages.docid: 157931
negative_passages.text: Contour integration of $\int \frac{dx} {(1+x^2)^{n+1}}$
negative_passages.docid: 95205
negative_passages.text: Integration of exponential and square root function
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: 41447
negative_passages.text: tough integral involving $\sin(x^2)$ and $\sinh^2 (x)$
negative_passages.docid: 142834
negative_passages.text: An integral : $\int_{-a}^a \frac{\cos(\pi n x/a)}{x^2+a^2}\mathrm dx$
negative_passages.docid: 42279
negative_passages.text: Evaluating the indefinite integral $ \int \sqrt{\tan x} ~ \mathrm{d}{x}. $
negative_passages.docid: 111956
negative_passages.text: Evaluating indefinite integrals of the form $\int \frac{x^2 \,dx}{a x^5 + b}$
negative_passages.docid: 95934
negative_passages.text: How to integrate $\int\frac{1}{\sqrt{1+x^3}}\mathrm dx$?
negative_passages.docid: 141387
negative_passages.text: Reduction Integration of $I_n=\int{\frac{x^n}{\sqrt{x^2+a^2}} dx}$
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: 21616
negative_passages.text: Calculate integral $\int_{-1}^{1} (1-x^2)^n dx $