query: Separate numerator and denominator integral
positive_passages.docid: 147759
positive_passages.text: Integral $ \dfrac { \int_0^{\pi/2} (\sin x)^{\sqrt 2 + 1} dx} { \int_0^{\pi/2} (\sin x)^{\sqrt 2 - 1} dx} $
negative_passages.docid: 42789
negative_passages.text: Integrate by Partial Fractions or Substitution
negative_passages.docid: 57947
negative_passages.text: Calculate center of mass multiple integrals
negative_passages.docid: 12446
negative_passages.text: integral involving a periodic function
negative_passages.docid: 31529
negative_passages.text: Integrating $\int^2_{-2}\frac{x^2}{1+5^x}$
negative_passages.docid: 45803
negative_passages.text: Integral of Derivative squared
negative_passages.docid: 45841
negative_passages.text: integral of $\int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx$ using contour integration?
negative_passages.docid: 112868
negative_passages.text: calculate an integration by using residue theorem
negative_passages.docid: 63016
negative_passages.text: Integration of $\int\frac{1}{x^{4}+1}\mathrm dx$
negative_passages.docid: 112885
negative_passages.text: Integrate $1/x$ by parts.
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: 67655
negative_passages.text: Simpler way to compute a definite integral without resorting to partial fractions?
negative_passages.docid: 105976
negative_passages.text: Calculate the integral using another integral
negative_passages.docid: 15185
negative_passages.text: Simplest way to integrate $\int \frac{1}{1+\tan x}dx,$
negative_passages.docid: 127343
negative_passages.text: Trigonometric integral involving the fractional part function
negative_passages.docid: 103164
negative_passages.text: Calculate Integral using residue theorem
negative_passages.docid: 102156
negative_passages.text: Integral of $\int_0^{\pi/2} \frac {\sqrt{\sin x}}{\sqrt {\sin x} + \sqrt {\cos x}}$dx