query: How to integrate $\int_{-\pi/4}^{\pi/4} (\cos(t) + \sqrt{1 + t^2}\cos^3(t)\sin^3(t))\;\mathrm{d}t$.
positive_passages.docid: 16712
positive_passages.text: Evaluate $\int_{-\pi/4}^{\pi/4}(\cos(t)+\sqrt{1+t^2}\cos(t)^3\sin (t)^3)dt$
negative_passages.docid: 20016
negative_passages.text: How to integrate $\int_0^{\pi/2}\frac{\sin^nx}{\sin^nx+\cos^nx}dx$?
negative_passages.docid: 49203
negative_passages.text: Evaluating $\int \sqrt{1 + t^2} dt$?
negative_passages.docid: 60491
negative_passages.text: Evaluate $ \int_{25\pi/4}^{53\pi/4}\frac{1}{(1+2^{\sin x})(1+2^{\cos x})}dx $
negative_passages.docid: 63016
negative_passages.text: Integration of $\int\frac{1}{x^{4}+1}\mathrm dx$
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: 82113
negative_passages.text: Solve $\int cos{\sqrt x} \ dx$ using a combination of substitution and integration by parts
negative_passages.docid: 36586
negative_passages.text: Evaluating $\frac{1}{2\pi}\int_{0}^{2\pi}\frac{1}{1-2t\cos\theta +t^2}d\theta$
negative_passages.docid: 122395
negative_passages.text: Integrating $\sec\theta\tan^2\theta d\,\theta$
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: 150843
negative_passages.text: Evaluation of $\int_0^{\pi/4} \sqrt{\tan x} \sqrt{1-\tan x}\,\,dx$
negative_passages.docid: 130736
negative_passages.text: Integrating $\int^0_\pi \frac{x \sin x}{1+\cos^2 x}$
negative_passages.docid: 114956
negative_passages.text: Integrate $\int \cos^4 x\,\mathrm dx.$
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: 90573
negative_passages.text: Indefinite integral $\int(\sin x)^2/(x\cdot\cos x-\sin x)^2\,dx$
negative_passages.docid: 12859
negative_passages.text: Find $\int \frac{x^3}{x^2-1} \:\mathrm{d}x$
negative_passages.docid: 61339
negative_passages.text: Integrating trigonometric function problem $\int \frac{3\sin x+2\cos x}{2\sin x+3\cos x}dx$