query: Problem evaluating $ \int_{0}^{\pi/2}\frac{x}{\tan x}dx $
positive_passages.docid: 20476
positive_passages.text: Today a student asked me $\int \ln (\sin x) \, dx.$
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: 143734
negative_passages.text: Evaluating $\int \frac{\sin\left(x\right)}{1+x^2}dx$
negative_passages.docid: 12604
negative_passages.text: Evaluate $\int_0^\pi xf(\sin x)dx$
negative_passages.docid: 117446
negative_passages.text: calculation of $\int_{0}^{1}\tan^{-1}(1-x+x^2)dx$
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: 97582
negative_passages.text: How do I evaluate this integral $\int_0^\pi{\frac{{{x^2}}}{{\sqrt 5-2\cos x}}}\operatorname d\!x$?
negative_passages.docid: 105423
negative_passages.text: Why doesn't every integral from 0 to $2\pi$ equal zero?
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: 2411
negative_passages.text: Integrate $\int_0^{\pi/2} \frac{1}{1+\tan^\alpha{x}}\,\mathrm{d}x$
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: 144811
negative_passages.text: Calculate $\int_0^{2\pi} \frac{1}{2+\sin(x)} \ dx$
negative_passages.docid: 61443
negative_passages.text: So close yet so far Finding $\int \frac {\sec x \tan x}{3x+5} dx$
negative_passages.docid: 31063
negative_passages.text: Evaluating $\int_0^2(\tan^{-1}(\pi x)-\tan^{-1} x)\,\mathrm{d}x$
negative_passages.docid: 51488
negative_passages.text: Evaluating $\int^\pi_{-\pi} \cos^3(x) \cos(ax)~dx$
negative_passages.docid: 44059
negative_passages.text: Evaluating $\int_{-1}^{1}\frac{\arctan{x}}{1+x}\ln{\left(\frac{1+x^2}{2}\right)}dx$
negative_passages.docid: 106544
negative_passages.text: Solve $ \frac{2}{\pi}\int_{-\pi}^\pi\frac{\sin\frac{9x}{2}}{\sin\frac{x}{2}}dx $