query: Find $\int{ {e}^x\cdot\cos(x) }dx$
positive_passages.docid: 22099
positive_passages.text: Integrate $e^{ax}\sin(bx)?$
negative_passages.docid: 104138
negative_passages.text: How to integrate $\int\limits_0^\infty e^{-a x^2}\cos(b x) dx$ where $a>0$
negative_passages.docid: 130058
negative_passages.text: Evaluate $\int_0^{\pi} e^{a\cos(t)}\cos(a\sin t)dt$
negative_passages.docid: 40881
negative_passages.text: Evaluate $\int_{0}^{+\infty }{\left( \frac{x}{{{\text{e}}^{x}}-{{\text{e}}^{-x}}}-\frac{1}{2} \right)\frac{1}{{{x}^{2}}}\text{d}x}$
negative_passages.docid: 107296
negative_passages.text: How do I prove $\int_{-\infty}^{\infty}{\cos(x+a)\over (x+b)^2+1}dx={\pi\over e}{\cos(a-b)}$?
negative_passages.docid: 28053
negative_passages.text: Integral of $\sin(e^t)dt$
negative_passages.docid: 63988
negative_passages.text: General formula for evaluating integrals of the form $\displaystyle\int_0^\infty x^ae^{-bx}dx$
negative_passages.docid: 152184
negative_passages.text: Find expectation of $\frac{X_1 + \cdots + X_m}{X_1 + \cdots + X_n}$ when $X_1,\ldots,X_n$ are i.i.d
negative_passages.docid: 113514
negative_passages.text: Solving $E=\frac{1}{\sin10^\circ}-\frac{\sqrt3}{\cos10^\circ}$
negative_passages.docid: 84826
negative_passages.text: Evaluating $\int_0^{2 \pi} e^{\cos x} \cos (nx - \sin x) \,dx$ using complex analysis
negative_passages.docid: 106878
negative_passages.text: How to integrate $\int \frac{e^x dx}{1\,+\,e^{2x}}$
negative_passages.docid: 99033
negative_passages.text: How to solve the definite integral $\int_{-4}^{-2}e^{-x}\,dx$?
negative_passages.docid: 109385
negative_passages.text: Evaluating the integral $\int_{-\ln 2}^{\ln 2} e^{-x}(\sin x+x)^{1/3}dx$
negative_passages.docid: 100194
negative_passages.text: Calculating $ \int _{0} ^{\infty} \frac{x^{3}}{e^{x}-1}\;dx$
negative_passages.docid: 76129
negative_passages.text: Evaluate $\int_0^\infty\frac{\sin(\varphi_1x)}x\frac{\sin\varphi_2x}x\cdots\frac{\sin\varphi_nx}x\frac{\sin(ax)}x\cos(a_1x)\cdots\cos(a_mx) \, dx$
negative_passages.docid: 43484
negative_passages.text: Integration by parts: $\int e^{ax}\cos(bx)\,dx$
negative_passages.docid: 10806
negative_passages.text: Find the value of $\int_{-\infty}^\infty \int_{-\infty}^\infty e^{-(x^2+xy+y^2)} \, dx\,dy$