query: How to calculate $\int \frac{1}{\sqrt{\sin x\cos^7x}}dx$?
positive_passages.docid: 26814
positive_passages.text: Solve $\int \frac{1}{\sin ^{\frac{1}{2}}x \cos^{\frac{7}{2}}x}dx$
negative_passages.docid: 43699
negative_passages.text: How do I integrate $\int \frac{dx}{\sin^3 x + \cos^3 x}$?
negative_passages.docid: 59667
negative_passages.text: Evaluating $\int_0^\infty\frac{\sin(x)}{x^2+1}\, dx$
negative_passages.docid: 99584
negative_passages.text: Evaluation of $\int \frac{\sqrt{\sin ^4x+\cos ^4x}}{\sin ^3x \cos x }dx$
negative_passages.docid: 92898
negative_passages.text: How to integrate $\sqrt{1-\sin 2x}$?
negative_passages.docid: 12653
negative_passages.text: Prove $\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$
negative_passages.docid: 67340
negative_passages.text: Integrate $\int \frac{dx}{\sqrt{\sin^3x\sin(x+\alpha)}}$
negative_passages.docid: 145403
negative_passages.text: Stuck in integration: $\int {\frac{dx}{( 1+\sqrt {x})\sqrt{(x-{x}^2)}}}$
negative_passages.docid: 53438
negative_passages.text: I need assistance in integrating $ \frac{x \sin x}{1+(\cos x)^2}$
negative_passages.docid: 8642
negative_passages.text: Calculate $ \int_{-2}^{0} \frac{x}{\sqrt{e^x+(x+2)^2}} dx $
negative_passages.docid: 154219
negative_passages.text: Help with integral $\int\frac{1}{\sqrt{\tan x}}dx$
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: 147641
negative_passages.text: How to evaluate $\int \frac { \sin x+\cos x }{ \sin^4 x+\cos^4x}\, dx$?
negative_passages.docid: 116219
negative_passages.text: How can I find  $\int\frac1{\sqrt[4]{1+x^4}}\mathrm dx$?
negative_passages.docid: 80736
negative_passages.text: How to integrate $\int\frac{\sqrt{1+x^2}}{x}\,\mathrm dx$
negative_passages.docid: 126054
negative_passages.text: calculate $\int_o^\pi \frac{x\sin x}{1+\cos^2x} \,dx$
negative_passages.docid: 60709
negative_passages.text: How do I get $\cos{\theta} \lt \frac{\sin{\theta}}{\theta} \lt 1$?