query: $\int_{0}^{2\pi}\frac{d\theta}{a+b\sin\theta}$ where $a,b>0$
positive_passages.docid: 149866
positive_passages.text: Evaluating $\int_0^{2\pi} \frac {\cos(\theta)}{5-3\cos(\theta)} \, d\theta$ using residue theorem
negative_passages.docid: 105619
negative_passages.text: Finding $\int_{0}^{\pi/2} \frac{\tan x}{1+m^2\tan^2{x}} \mathrm{d}x$
negative_passages.docid: 16800
negative_passages.text: Integrating $\int_0^{2\pi} \frac1{a\cos(t)+b\sin(t)+c}dt$ with $\sqrt{a^2+b^2}=1<c$
negative_passages.docid: 74241
negative_passages.text: Integrate square of the log-sine integral: $\int_0^{\frac{\pi}{2}}\ln^{2}(\sin(x))dx$
negative_passages.docid: 7835
negative_passages.text: Tricky elementary integral $\int_{0}^{\frac{\pi}{2}}x\cot(x)dx$.
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: 1416
negative_passages.text: closed form of $\int_{0}^{2\pi}\frac{dx}{(a^2\cos^2x+b^2\sin^2x)^n}$
negative_passages.docid: 144811
negative_passages.text: Calculate $\int_0^{2\pi} \frac{1}{2+\sin(x)} \ dx$
negative_passages.docid: 71988
negative_passages.text: Evaluate $\int_0^{2\pi} \frac{\sin^2\theta}{5+4\cos\theta}\,\mathrm d\theta$
negative_passages.docid: 18672
negative_passages.text: Integrate $\int_{0}^{\pi}{\frac{x\cos{x}}{1+\sin^{2}{x}}dx}$
negative_passages.docid: 54638
negative_passages.text: Integral $\int^{ \pi /2}_{0} \ln (\sin x)\ dx$
negative_passages.docid: 157364
negative_passages.text: $\int_{-2}^{2} \sin(x^5)e^{(x^8\sin(x^4))} dx$
negative_passages.docid: 135653
negative_passages.text: An integral$\frac{1}{2\pi}\int_0^{2\pi}\log|\exp(i\theta)-a|\text{d}\theta=0$ which I can calculate but can't understand it.
negative_passages.docid: 6852
negative_passages.text: Integral of $\int \frac{x \sin{x} \cos{x}}{(a^2 \sin^2 x + b^2 \cos^2 x)^2} dx $
negative_passages.docid: 32672
negative_passages.text: Integrating :$\int_{0}^{1} \frac{x^{b}-x^{a}}{\log(x)}\sin(\log(x))dx$
negative_passages.docid: 27002
negative_passages.text: Evaluating $\int\limits_0^{\pi} \frac{dx}{1+2\sin^2x}$
negative_passages.docid: 71742
negative_passages.text: integrate $\int_0^{2\pi} e^{\cos \theta} \cos( \sin \theta) d\theta$