query: Evaluate $\int \frac{1}{2+\sin x+\cos x}dx.$
positive_passages.docid: 146579
positive_passages.text: What is the right first step to take when integrating $1/(2+ \sin x + \cos x)$?
negative_passages.docid: 70013
negative_passages.text: How to calculate $\int \frac{x^2 }{(x^2+1)^2} dx$?
negative_passages.docid: 131310
negative_passages.text: Evaluating $\dfrac{1}{\sin(2x)} + \dfrac{1}{\sin(4x)} + \dfrac{1}{\sin(8x)} + \dfrac{1}{\sin(16x)}$
negative_passages.docid: 24182
negative_passages.text: Evaluating $\int_{0}^{\infty}\frac{\sin^{2n+1}x}{x}\mathrm{d}x$
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: 147641
negative_passages.text: How to evaluate $\int \frac { \sin x+\cos x }{ \sin^4 x+\cos^4x}\, dx$?
negative_passages.docid: 76129
negative_passages.text: Evaluate $\int_0^\infty\frac{\sin(\varphi_1x)}x\frac{\sin\varphi_2x}x\cdots\frac{\sin\varphi_nx}x\frac{\sin(ax)}x\cos(a_1x)\cdots\cos(a_mx) \, dx$
negative_passages.docid: 122913
negative_passages.text: Evaluate $\int \frac{\sec^{2}{x}}{(\sec{x} + \tan{x})^{5/2}} \ \mathrm dx$
negative_passages.docid: 125735
negative_passages.text: How do I evaluate $\int_{1/3}^3 \frac{\arctan x}{x^2 - x + 1} \; dx$?
negative_passages.docid: 88670
negative_passages.text: Evaluating $\int \frac{1}{{x^4+1}} dx$
negative_passages.docid: 153867
negative_passages.text: Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$
negative_passages.docid: 127756
negative_passages.text: Integrate $\int \sin (2x) \cos (2x)\,dx$
negative_passages.docid: 130058
negative_passages.text: Evaluate $\int_0^{\pi} e^{a\cos(t)}\cos(a\sin t)dt$
negative_passages.docid: 67340
negative_passages.text: Integrate $\int \frac{dx}{\sqrt{\sin^3x\sin(x+\alpha)}}$
negative_passages.docid: 95068
negative_passages.text: Integral of $\frac{1}{2x}$
negative_passages.docid: 155422
negative_passages.text: Evaluating $\int_{0}^{\frac{\pi}{2}}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}\, \mathrm{d}x$
negative_passages.docid: 29425
negative_passages.text: $\int_{0}^{\infty}\frac{\sin^{2n+1}(x)}{x} \mathrm {d}x$ Evaluate Integral