query: Integral: $\int_0^\infty \frac{|\sin (2x)| - | \sin (3x) |}x dx$
positive_passages.docid: 717
positive_passages.text: Proof of Frullani's theorem
negative_passages.docid: 108554
negative_passages.text: Integrating $\int_0^\infty\frac{1}{1+x^6}dx$
negative_passages.docid: 65337
negative_passages.text: Compute $\int_{0}^{\infty}\frac{x\sin 2x}{9+x^{2}} \, dx$
negative_passages.docid: 36366
negative_passages.text: Prove $\int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3}$
negative_passages.docid: 158279
negative_passages.text: $\int_0^{\pi/2}\ln(\sin(x))$?
negative_passages.docid: 85949
negative_passages.text: Integral involving logarithm: $\int_0^\infty \frac{ \ln x}{(x+a)(x+b)} dx$
negative_passages.docid: 4971
negative_passages.text: $\int_{0}^{1}\frac{1-x}{1+x}.\frac{dx}{\sqrt{x+x^2+x^3}}$
negative_passages.docid: 100569
negative_passages.text: Evaluating the improper integral $\int_{0}^{\infty} \frac{x^3}{e^{x}-1} dx$
negative_passages.docid: 62173
negative_passages.text: How do I show that $\int_0^\infty \frac{\sin(ax) \sin(bx)}{x^{2}} \, \mathrm dx = \pi \min(a,b)/2$
negative_passages.docid: 148613
negative_passages.text: Integrate $\int_{0}^{1}{x^{-x}(1-x)^{x-1}\sin{\pi x}dx}$
negative_passages.docid: 88372
negative_passages.text: Integrate : $\int \frac{\sin x}{\sin4x} \,dx$
negative_passages.docid: 86923
negative_passages.text: Evaluating the integral $\int_0^\infty \frac{x \sin rx }{a^2+x^2} dx$ using only real analysis
negative_passages.docid: 18672
negative_passages.text: Integrate $\int_{0}^{\pi}{\frac{x\cos{x}}{1+\sin^{2}{x}}dx}$
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: 127756
negative_passages.text: Integrate $\int \sin (2x) \cos (2x)\,dx$
negative_passages.docid: 63650
negative_passages.text: Evaluating the contour integral $\int_{0}^{\infty}\frac{\sin^{3}(x)}{x^{3}}\mathrm dx$
negative_passages.docid: 76129
negative_passages.text: Evaluate $\int_0^\infty\frac{\sin(\varphi_1x)}x\frac{\sin\varphi_2x}x\cdots\frac{\sin\varphi_nx}x\frac{\sin(ax)}x\cos(a_1x)\cdots\cos(a_mx) \, dx$