query: Evaluate $\int_0^{\frac{\pi}{2}} \frac{\sin^3(x)}{\cos^3(x)+\sin^3(x)} dx$
positive_passages.docid: 151063
positive_passages.text: Calculate $\int_{0}^{\frac{\pi}{2}}\frac{\sin^{3}(t)}{\sin^{3}(t)+\cos^{3}(t)}dt$ by hands
negative_passages.docid: 26096
negative_passages.text: Evaluating $\int \frac{\sin{x}+\cos{x}}{\sin^4{x}+\cos^4{x}} \mathrm dx$
negative_passages.docid: 74822
negative_passages.text: How to evaluate $\int_{0}^{\pi }\theta \ln\tan\frac{\theta }{2} \, \mathrm{d}\theta$
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: 51488
negative_passages.text: Evaluating $\int^\pi_{-\pi} \cos^3(x) \cos(ax)~dx$
negative_passages.docid: 51971
negative_passages.text: How to evaluate the integral $\int e^{x^3}dx $
negative_passages.docid: 91212
negative_passages.text: Evaluate $\int \cos^3 x\;\sin^2 xdx$
negative_passages.docid: 149866
negative_passages.text: Evaluating $\int_0^{2\pi} \frac {\cos(\theta)}{5-3\cos(\theta)} \, d\theta$ using residue theorem
negative_passages.docid: 151563
negative_passages.text: Evaluate: $\int_{0}^{\pi}\frac{\cos 2017x}{5-4\cos x}dx$
negative_passages.docid: 59667
negative_passages.text: Evaluating $\int_0^\infty\frac{\sin(x)}{x^2+1}\, dx$
negative_passages.docid: 44398
negative_passages.text: How to compute $\int_0^{\pi/2}\frac{\sin^3 t}{\sin^3 t+\cos^3 t}dt$?
negative_passages.docid: 146338
negative_passages.text: How to evaluate $\int\frac{1+x^4}{(1-x^4)^{3/2}}dx$?
negative_passages.docid: 17454
negative_passages.text: Evaluate the integral $\int_0^n \frac{f(x)}{f(x) + f(n-x)}dx $
negative_passages.docid: 100485
negative_passages.text: How do I evaluate the integral $\int_0^{\infty}\frac{x^5\sin(x)}{(1+x^2)^3}dx$?
negative_passages.docid: 3704
negative_passages.text: Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$?
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: 1416
negative_passages.text: closed form of $\int_{0}^{2\pi}\frac{dx}{(a^2\cos^2x+b^2\sin^2x)^n}$