query: Evaluate the indefinite integral of $\int\left(a^2-\frac{\sin {(a)}}{a^{2} + 1}-a\cos{(a)}\right)\,da$
positive_passages.docid: 143734
positive_passages.text: Evaluating $\int \frac{\sin\left(x\right)}{1+x^2}dx$
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: 145590
negative_passages.text: Compute the integral $\int\frac{dx}{(x^2-x+1)\sqrt{x^2+x+1}}$
negative_passages.docid: 146870
negative_passages.text: Integrals depending on a parameter: $\int_{0}^{\pi/2} \ln(a^2\sin^2{x} + \cos^2{x})dx $
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: 147759
negative_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: 31063
negative_passages.text: Evaluating $\int_0^2(\tan^{-1}(\pi x)-\tan^{-1} x)\,\mathrm{d}x$
negative_passages.docid: 142619
negative_passages.text: Evaluating the complex integral $\int_{|z|=2}^{}\frac{1}{z^2+1}dz$
negative_passages.docid: 104094
negative_passages.text: Integral of $\frac{1}{(1+x^2)^2}$
negative_passages.docid: 142516
negative_passages.text: Evaluating the integral, $\int_{0}^{\infty} \ln\left(1 - e^{-x}\right) \,\mathrm dx $
negative_passages.docid: 24808
negative_passages.text: How to evaluate the integral $\int \sqrt{1+\sin(x)} dx$
negative_passages.docid: 86923
negative_passages.text: Evaluating the integral $\int_0^\infty \frac{x \sin rx }{a^2+x^2} dx$ using only real analysis
negative_passages.docid: 100401
negative_passages.text: Evaluate $\int \frac{1}{(x^2+1)^2}dx$
negative_passages.docid: 122361
negative_passages.text: Evaluate $\int_0^1\left(\frac{1}{\ln x} + \frac{1}{1-x}\right)^2 \mathrm dx$
negative_passages.docid: 65847
negative_passages.text: To evaluate $\int_{0}^\pi \frac {\sin^2 x}{a^2-2ab \cos x + b^2}\mathrm dx$?
negative_passages.docid: 17337
negative_passages.text: Double Integral $\int\limits_0^a\int\limits_0^a\frac{dx\,dy}{(x^2+y^2+a^2)^\frac32}$
negative_passages.docid: 84683
negative_passages.text: integrate $dx/(a^2 \cos^2x+b^2 \sin^2x)^2$