query: Is $\int^0_0 x^{-1} dx$ defined?
positive_passages.docid: 21522
positive_passages.text: This integral is defined ? $\displaystyle\int_0^0\frac 1x\:dx$
negative_passages.docid: 115089
negative_passages.text: Definite Integral: $\int_0^1\frac{x^{2} -1}{\log x}\,dx$
negative_passages.docid: 93610
negative_passages.text: What is $\int_0^1 \frac{\log \left(1-x^2\right) \sin ^{-1}(x)^2}{x^2} \, dx$?
negative_passages.docid: 96554
negative_passages.text: Why is $x^0 = 1$ except when $x = 0$?
negative_passages.docid: 104691
negative_passages.text: Integration of $\int_{0}^{1} \frac{x^k}{1-x} dx$
negative_passages.docid: 86054
negative_passages.text: $r+r^{-1}$ integral implies $r^n+r^{-n}$ integral
negative_passages.docid: 46310
negative_passages.text: Showing that $ \int_{0}^{1} \frac{x-1}{\ln(x)} \mathrm dx=\ln2 $
negative_passages.docid: 71953
negative_passages.text: If $\int_0^1 f x^n dx=0, \forall n \in \mathbb{N} $, then $f\equiv 0.$
negative_passages.docid: 98710
negative_passages.text: Finding $\int_0^{\infty}xe^{-\lambda x} \, dx$
negative_passages.docid: 63590
negative_passages.text: Let $g$ be a function from $(0, 1)$ to $\mathbb{R}$ and $\int_0^1 g^2(x)dx$ finite. Does this imply that $\int_0^1 g(x)dx$ is finite?
negative_passages.docid: 53518
negative_passages.text: Integrating : $\int_0^1 {\frac {x^a-x^b} {\ln x} dx}$
negative_passages.docid: 89028
negative_passages.text: Evaluate the integral $\int e^{-x}x^n dx$
negative_passages.docid: 33989
negative_passages.text: If $\int_0^1 f(x)x^n \ dx=0$ for every $n$, then $f=0$.
negative_passages.docid: 109416
negative_passages.text: How to calculate $\int_0^1 \frac{\ln(1-x)}{x} dx$?
negative_passages.docid: 70790
negative_passages.text: Evaluation of $\lim_{q \to 0} (\int_0^1 |f|^q)^{1/q} $ for $f \in L^1([0,1])$.
negative_passages.docid: 506
negative_passages.text: Finding $\int x^xdx$
negative_passages.docid: 138054
negative_passages.text: Proving that $\int_0^1 f(x)e^{nx}\,{\rm d}x = 0$ for all $n\in\mathbb{N}_0$ implies $f(x) = 0$