query: Evaluate the integral $\int^{\frac{\pi}{2}}_0 \frac{\sin^3x}{\sin^3x+\cos^3x}\,\mathrm dx$.
positive_passages.docid: 44398
positive_passages.text: How to compute $\int_0^{\pi/2}\frac{\sin^3 t}{\sin^3 t+\cos^3 t}dt$?
negative_passages.docid: 16712
negative_passages.text: Evaluate $\int_{-\pi/4}^{\pi/4}(\cos(t)+\sqrt{1+t^2}\cos(t)^3\sin (t)^3)dt$
negative_passages.docid: 61740
negative_passages.text: Evaluate the integration : $\int\sqrt{\frac{(1-\sin x)(2-\sin x)}{(1+\sin x)(2+\sin x)}}dx$
negative_passages.docid: 154065
negative_passages.text: $\int_{\frac{1}{3}\pi}^{\frac{2}{3}\pi} {\sin(x)\;dx}$ using Riemann sums?
negative_passages.docid: 91212
negative_passages.text: Evaluate $\int \cos^3 x\;\sin^2 xdx$
negative_passages.docid: 135447
negative_passages.text: Compute the integral $\int_0^{\frac\pi2}\frac{\mathrm d \theta}{\sqrt{\sin \theta}}$
negative_passages.docid: 130668
negative_passages.text: Evaluating the integral with trigonometric integrand
negative_passages.docid: 49306
negative_passages.text: Calculation of $\int_0^{\pi} \frac{\sin^2 x}{a^2+b^2-2ab \cos x}\mathrm dx$
negative_passages.docid: 27002
negative_passages.text: Evaluating $\int\limits_0^{\pi} \frac{dx}{1+2\sin^2x}$
negative_passages.docid: 145907
negative_passages.text: How do you evaluate this integral $\int \frac{6x^{3}+7x^2-12x+1}{\sqrt{x^2+4x+6}}dx$
negative_passages.docid: 37097
negative_passages.text: Integral $\int \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} dx$
negative_passages.docid: 151063
negative_passages.text: Calculate $\int_{0}^{\frac{\pi}{2}}\frac{\sin^{3}(t)}{\sin^{3}(t)+\cos^{3}(t)}dt$ by hands
negative_passages.docid: 60944
negative_passages.text: Evaluating an integral with ${\mathrm{d}t}$ in the numerator, $\int \frac{\mathrm{d}t}{\cos(t)^2}$.
negative_passages.docid: 80553
negative_passages.text: Show that,$\int_0^\pi \left|\frac{\sin nx}{x}\right|\mathrm{d}x \ge \frac{2}{\pi}\left(1+\frac12+\cdots+\frac{1}{n}\right)$
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: 71611
negative_passages.text: Evaluating $\int\sqrt{\frac{1-x^2}{1+x^2}}\mathrm dx$
negative_passages.docid: 18672
negative_passages.text: Integrate $\int_{0}^{\pi}{\frac{x\cos{x}}{1+\sin^{2}{x}}dx}$