query: Definite integral over a semicircular area $\int_0^{2a}\int_0^{\sqrt{2ax-x^2}}\frac{\phi'(y)(x^2+y^2)x}{\sqrt{4a^2x^2-(x^2+y^2)^2}}dy\,dx$.
positive_passages.docid: 17679
positive_passages.text: Evaluate the integral $\int_0^{2a}\int_0^\sqrt{2ax-x^2}\frac{\phi'(y)(x^2+y^2)x dxdy}{\sqrt{4a^2x^2-(x^2+y^2)^2}}$
negative_passages.docid: 120899
negative_passages.text: Integration with a constant "a": $ \int_0^a \frac1{\sqrt {a^2-x^2}} dx $
negative_passages.docid: 47793
negative_passages.text: Integral $\int_0^1\sqrt{1-x^4}dx$
negative_passages.docid: 177
negative_passages.text: How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$
negative_passages.docid: 80319
negative_passages.text: Integrate: $\int (x^2+a^2)^{-3/2} \cdot dx$
negative_passages.docid: 31063
negative_passages.text: Evaluating $\int_0^2(\tan^{-1}(\pi x)-\tan^{-1} x)\,\mathrm{d}x$
negative_passages.docid: 141688
negative_passages.text: Indefinite integral of $ \int \frac{x^3}{\sqrt{x^2+1}} \,\text{d}x$.
negative_passages.docid: 104094
negative_passages.text: Integral of $\frac{1}{(1+x^2)^2}$
negative_passages.docid: 135447
negative_passages.text: Compute the integral $\int_0^{\frac\pi2}\frac{\mathrm d \theta}{\sqrt{\sin \theta}}$
negative_passages.docid: 7042
negative_passages.text: Defined integral of $x^{\alpha} (1-x)^{\beta-1}$
negative_passages.docid: 74241
negative_passages.text: Integrate square of the log-sine integral: $\int_0^{\frac{\pi}{2}}\ln^{2}(\sin(x))dx$
negative_passages.docid: 17996
negative_passages.text: Integral $\int_0^1 \frac{\ln(x+\sqrt{1-x^2})}{x}dx$
negative_passages.docid: 85814
negative_passages.text: Quotient of two integrals $\frac{\int_0^\pi x^3\ln(\sin x)\,dx}{\int_0^\pi x^2\ln(\sqrt{2}(\sin x))\,dx}$
negative_passages.docid: 39629
negative_passages.text: Indefinite integration of $\int \frac{1}{1+\sqrt{x^2+2x+2}}dx$
negative_passages.docid: 1150
negative_passages.text: Indefinite Integral of $\sqrt{\sin x}$
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: 10319
negative_passages.text: Definite Integral $\int_{-\infty}^{\infty}\frac{x\sin x}{(x^2+a^2)(x^2+b^2)}\,\mathrm{d}x$