query: Integrate $\int e^{-x} \cos x \,\mathrm{d}x$
positive_passages.docid: 43484
positive_passages.text: Integration by parts: $\int e^{ax}\cos(bx)\,dx$
negative_passages.docid: 156215
negative_passages.text: Integral $\int\frac{2x^2}{2x\cos(2x)+(x^2-1)\sin(2x)} \mathrm d x$
negative_passages.docid: 63016
negative_passages.text: Integration of $\int\frac{1}{x^{4}+1}\mathrm dx$
negative_passages.docid: 80736
negative_passages.text: How to integrate $\int\frac{\sqrt{1+x^2}}{x}\,\mathrm dx$
negative_passages.docid: 60944
negative_passages.text: Evaluating an integral with ${\mathrm{d}t}$ in the numerator, $\int \frac{\mathrm{d}t}{\cos(t)^2}$.
negative_passages.docid: 67450
negative_passages.text: How do you integrate $e^{x^2}$?
negative_passages.docid: 24182
negative_passages.text: Evaluating $\int_{0}^{\infty}\frac{\sin^{2n+1}x}{x}\mathrm{d}x$
negative_passages.docid: 117602
negative_passages.text: How to evaluate $\int \cot^2(x) \;\mathrm dx$?
negative_passages.docid: 51488
negative_passages.text: Evaluating $\int^\pi_{-\pi} \cos^3(x) \cos(ax)~dx$
negative_passages.docid: 110343
negative_passages.text: Integrating $\rm x^ae^{-bx}$.
negative_passages.docid: 108396
negative_passages.text: Integral $\int_0^{\infty} \frac{\log x}{\cosh^2x} \ \mathrm{d}x = \log\frac {\pi}4- \gamma$
negative_passages.docid: 65093
negative_passages.text: Integrate $\int \sin^4x \cos^2x dx$
negative_passages.docid: 106878
negative_passages.text: How to integrate $\int \frac{e^x dx}{1\,+\,e^{2x}}$
negative_passages.docid: 82113
negative_passages.text: Solve $\int cos{\sqrt x} \ dx$ using a combination of substitution and integration by parts
negative_passages.docid: 69124
negative_passages.text: Integral $\int_{0}^{\infty}e^{-ax}\cos (bx)\operatorname d\!x$
negative_passages.docid: 142516
negative_passages.text: Evaluating the integral, $\int_{0}^{\infty} \ln\left(1 - e^{-x}\right) \,\mathrm dx $
negative_passages.docid: 75562
negative_passages.text: How to integrate $\int x^2 \sin^2(x)dx$