query: Use Integration by Parts to find $\int \cos x\cdot e^x\;dx$
positive_passages.docid: 43484
positive_passages.text: Integration by parts: $\int e^{ax}\cos(bx)\,dx$
negative_passages.docid: 99457
negative_passages.text: How to integrate $\int x\sin {(\sqrt{x})}\, dx$
negative_passages.docid: 51489
negative_passages.text: Simplifying the integral $\int\frac{dx}{(3 + 2\sin x - \cos x)}$ by an easy approach
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: 79279
negative_passages.text: Integral of cosec squared ($\operatorname{cosec}^2x$, $\csc^2x$)
negative_passages.docid: 122843
negative_passages.text: Finding $\int_0^\infty \frac{\cos(ax)-\cos(bx)}{x}dx$
negative_passages.docid: 43699
negative_passages.text: How do I integrate $\int \frac{dx}{\sin^3 x + \cos^3 x}$?
negative_passages.docid: 12537
negative_passages.text: How to Integrate this function $\int(1-x^2)^ndx$
negative_passages.docid: 41738
negative_passages.text: Best way to integrate $ \int_0^\infty \frac{e^{-at} - e^{-bt}}{t} \text{d}t $
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: 90313
negative_passages.text: Integrate $\int_0^\pi{{x\sin x}\over{1+\cos^2x}}dx$.
negative_passages.docid: 6483
negative_passages.text: Computing $\int_{0}^{\pi}\ln\left(1-2a\cos x+a^2\right) \, dx$
negative_passages.docid: 146737
negative_passages.text: Integrate $\iiint_E z\,dx\,dy\,dz$ in $E=\lbrace(x,y,z) : x^2+y^2+z^2 \leq 4, z \leq 1 \rbrace$
negative_passages.docid: 84683
negative_passages.text: integrate $dx/(a^2 \cos^2x+b^2 \sin^2x)^2$
negative_passages.docid: 126054
negative_passages.text: calculate $\int_o^\pi \frac{x\sin x}{1+\cos^2x} \,dx$
negative_passages.docid: 90339
negative_passages.text: Integral involving Cosine function
negative_passages.docid: 53554
negative_passages.text: Evaluate $\int \cos(\cos x)~dx$