query: What is the proof that $\int e^{-x^2} \cdot dx$ is not elementry.
positive_passages.docid: 3978
positive_passages.text: How can you prove that a function has no closed form integral?
negative_passages.docid: 25050
negative_passages.text: To prove that $(F,+)$ and $(F-\{0\},\cdot)$ are not isomorphic as groups.
negative_passages.docid: 83531
negative_passages.text: Prove $\iint_{x^{2}+y^{2} \leq 1} e^{x^{2}+y^{2}} d x d y \leq\left[\int_{-\frac{\sqrt{\pi}}{2}}^{\frac{\sqrt{\pi}}{2}} e^{x^{2}} d x\right]^{2} $
negative_passages.docid: 10366
negative_passages.text: Why do we not include $c$ in the computation of the definite integral?
negative_passages.docid: 87169
negative_passages.text: Convergence of $\int_{1}^{\infty}x\cdot \sin{(e^x})\,dx$
negative_passages.docid: 94395
negative_passages.text: Integral: $\int_{-\infty}^{\infty} x^2 e^{-x^2}\mathrm dx$
negative_passages.docid: 67168
negative_passages.text: Loopy integral $\int xe^x\sin(x)$
negative_passages.docid: 143113
negative_passages.text: Non-inductive, not combinatorial proof of $\sum_{i \mathop = 0}^n \binom n i^2 = \binom {2 n} n$
negative_passages.docid: 107254
negative_passages.text: Real analysis question $e^{-1/x^2}$
negative_passages.docid: 21843
negative_passages.text: Proving a function is not Riemann integrable
negative_passages.docid: 109901
negative_passages.text: Computing $\int_0^\infty\frac1{(x+1)(x+2)\cdots(x+n)}\mathrm dx $
negative_passages.docid: 29680
negative_passages.text: How to determine $\int x^2 e^{-x^2}\mathrm dx$?
negative_passages.docid: 7835
negative_passages.text: Tricky elementary integral $\int_{0}^{\frac{\pi}{2}}x\cot(x)dx$.
negative_passages.docid: 19962
negative_passages.text: Why is $\infty \cdot 0$ not clearly equal to $0$?
negative_passages.docid: 89028
negative_passages.text: Evaluate the integral $\int e^{-x}x^n dx$
negative_passages.docid: 1626
negative_passages.text: How do we prove $\int_I\int_x^1\frac{1}{t}f(t)\text{ dt}\text{ dx}=\int_If(x)\text{ dx}$
negative_passages.docid: 1392
negative_passages.text: $\int_{0}^{\infty}{\left(x^3\cdot(e^x-1)^{-1} \right)}dx$