query: Integral with powers of sine and cosine
positive_passages.docid: 9653
positive_passages.text: Evaluate the integral $\int^{\frac{\pi}{2}}_0 \frac{\sin^3x}{\sin^3x+\cos^3x}\,\mathrm dx$.
negative_passages.docid: 89387
negative_passages.text: Integrate : $\int \frac{x^2}{(x\cos x -\sin x)(x\sin x +\cos x)}dx$
negative_passages.docid: 518
negative_passages.text: What is the integral of $\int e^x\,\sin x\,\,dx$?
negative_passages.docid: 148613
negative_passages.text: Integrate $\int_{0}^{1}{x^{-x}(1-x)^{x-1}\sin{\pi x}dx}$
negative_passages.docid: 12604
negative_passages.text: Evaluate $\int_0^\pi xf(\sin x)dx$
negative_passages.docid: 148826
negative_passages.text: Integral of $ 1 \, / \, (1 + a \, \cos(x) )$
negative_passages.docid: 92898
negative_passages.text: How to integrate $\sqrt{1-\sin 2x}$?
negative_passages.docid: 86712
negative_passages.text: Use rectangular contour to integrate $\int_{0}^{\infty}\frac{\sin(ax)}{e^{2\pi x}-1}dx$
negative_passages.docid: 90313
negative_passages.text: Integrate $\int_0^\pi{{x\sin x}\over{1+\cos^2x}}dx$.
negative_passages.docid: 30127
negative_passages.text: Integration of sqrt Sin x dx
negative_passages.docid: 20746
negative_passages.text: Evaluating $\int P(\sin x, \cos x) \text{d}x$
negative_passages.docid: 16639
negative_passages.text: How to integrate $ \int_0^\infty \sin x \cdot x ^{-1/3} dx$ (using Gamma function)
negative_passages.docid: 90573
negative_passages.text: Indefinite integral $\int(\sin x)^2/(x\cdot\cos x-\sin x)^2\,dx$
negative_passages.docid: 23685
negative_passages.text: Integrating $\int \sin^n{x} \ dx$
negative_passages.docid: 122233
negative_passages.text: Trig Fresnel Integral
negative_passages.docid: 144811
negative_passages.text: Calculate $\int_0^{2\pi} \frac{1}{2+\sin(x)} \ dx$
negative_passages.docid: 140386
negative_passages.text: Integrate $\int {\dfrac{x^2+\left(n-1\right)n}{\left(x\sin x+n\cos x\right)^2}}dx $