query: Integration of a function involving algebraic and trigonometric functions
positive_passages.docid: 153867
positive_passages.text: Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$
negative_passages.docid: 136385
negative_passages.text: Integrate $ \int_{0}^{\frac{\pi}{4}}\tan^{-1}\left(\frac{\sqrt{2}\cos3 \phi}{\left(2\cos 2 \phi+ 3\right)\sqrt{\cos 2 \phi}}\right)d\phi$
negative_passages.docid: 31922
negative_passages.text: Integral of $\sin x \cos x$ using two methods differs by a constant?
negative_passages.docid: 26096
negative_passages.text: Evaluating $\int \frac{\sin{x}+\cos{x}}{\sin^4{x}+\cos^4{x}} \mathrm dx$
negative_passages.docid: 67340
negative_passages.text: Integrate $\int \frac{dx}{\sqrt{\sin^3x\sin(x+\alpha)}}$
negative_passages.docid: 71742
negative_passages.text: integrate $\int_0^{2\pi} e^{\cos \theta} \cos( \sin \theta) d\theta$
negative_passages.docid: 77810
negative_passages.text: Solving Trigonometric Derivatives
negative_passages.docid: 6573
negative_passages.text: Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$
negative_passages.docid: 144018
negative_passages.text: Integration by parts for f(x).g(x)
negative_passages.docid: 98678
negative_passages.text: Finding the following definite and indefinite integrals
negative_passages.docid: 14279
negative_passages.text: Indefinite Integral with "sin" and "cos": $\int\frac{3\sin(x) + 2\cos(x)}{2\sin(x) + 3\cos(x)} \; dx $
negative_passages.docid: 89387
negative_passages.text: Integrate : $\int \frac{x^2}{(x\cos x -\sin x)(x\sin x +\cos x)}dx$
negative_passages.docid: 90339
negative_passages.text: Integral involving Cosine function
negative_passages.docid: 18672
negative_passages.text: Integrate $\int_{0}^{\pi}{\frac{x\cos{x}}{1+\sin^{2}{x}}dx}$
negative_passages.docid: 129318
negative_passages.text: Integrate via substitution and derivation rule
negative_passages.docid: 65093
negative_passages.text: Integrate $\int \sin^4x \cos^2x dx$
negative_passages.docid: 103487
negative_passages.text: Integration of the cardinal sine