query: Integral of the product of $x^k$ and the upper half circle of radius 2.
positive_passages.docid: 154910
positive_passages.text: Calculus Reduction Formula
negative_passages.docid: 114418
negative_passages.text: A deduction from $x^n-1=(x^2-1)\prod_{k=1}^{(n-2)/2}[x^2-2x\cos{\frac{2k\pi}{n}}+1]$
negative_passages.docid: 43593
negative_passages.text: half-derivative of $x^2$
negative_passages.docid: 136652
negative_passages.text: Closed form expression for the product $\prod\limits_{k=1}^{n}\left(1 - \frac{1}{ak}\right)$
negative_passages.docid: 23919
negative_passages.text: Trying to evaluate $\prod_{k=1}^{n-1}(1-e^{2k\pi i/n})$ for my complex analysis homework
negative_passages.docid: 24589
negative_passages.text: Integral of $1/(x^2-1)^2$
negative_passages.docid: 49554
negative_passages.text: Physical meaning of this integral in $k$-space
negative_passages.docid: 2776
negative_passages.text: What can be said about the integral part of $(a+\sqrt{b})^n $
negative_passages.docid: 3199
negative_passages.text: Number of positive integral solution of product $x_{1} \cdot x_{2} \cdot x_{3}\cdot x_{4}\cdot x_{5}=1050$ is
negative_passages.docid: 110343
negative_passages.text: Integrating $\rm x^ae^{-bx}$.
negative_passages.docid: 44737
negative_passages.text: $ \int_{-\infty}^{\infty} x^4 e^{-ax^2} dx$
negative_passages.docid: 90921
negative_passages.text: Product of two primitive polynomials
negative_passages.docid: 70375
negative_passages.text: Wallis Product with integrals
negative_passages.docid: 13864
negative_passages.text: $\prod_{k=0}^{\infty} \cos(x \cdot 2^{-k}).$
negative_passages.docid: 34440
negative_passages.text: Finding Value of the Infinite Product $\prod \Bigl(1-\frac{1}{n^{2}}\Bigr)$
negative_passages.docid: 147144
negative_passages.text: Integral of triangular relation
negative_passages.docid: 154183
negative_passages.text: Proof of a Ramanujan Integral