query: $I_n=\int_0^1 \frac{x^n}{\sqrt{1+x^2}}$, find $nI_n$
positive_passages.docid: 146528
positive_passages.text: Define $I_n=\int_0^1\frac{x^n}{\sqrt{x^2+1}}dx$ for every $n\in\mathbb{N}$. Prove that $\lim_{n\to\infty}nI_n=\frac{1}{\sqrt 2}$.
negative_passages.docid: 57686
negative_passages.text: Finding $ \int^1_0 \frac{\ln(1+x)}{x}dx$
negative_passages.docid: 121071
negative_passages.text: Calculation of $\int^{\pi/2}_{0}\cos^{n}(x)\cos (nx)\,dx$, where $n\in \mathbb{N}$
negative_passages.docid: 4971
negative_passages.text: $\int_{0}^{1}\frac{1-x}{1+x}.\frac{dx}{\sqrt{x+x^2+x^3}}$
negative_passages.docid: 133160
negative_passages.text: Closed form for $\int_0^\infty\frac{1}{(1+x^2)^s}\,dx$ when $s\in (0.5,\infty)\setminus\mathbb{N}$
negative_passages.docid: 88708
negative_passages.text: An integration of product $(1-x^n)$
negative_passages.docid: 12967
negative_passages.text: Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer.
negative_passages.docid: 115375
negative_passages.text: Indefinite integral of $e^{x^n}$
negative_passages.docid: 64800
negative_passages.text: Evaluate $\int_0^1 \log \left( \frac{x^2+\sqrt{3}x+1}{x^2-\sqrt{3}x+1} \right) \frac{dx}{x} $
negative_passages.docid: 58909
negative_passages.text: Evaluation of $\int\frac{dx}{x+ \sqrt{x^2-x+1}}$
negative_passages.docid: 104094
negative_passages.text: Integral of $\frac{1}{(1+x^2)^2}$
negative_passages.docid: 109887
negative_passages.text: How to evaluate $\int_0^1 (\arctan x)^2 \ln(\frac{1+x^2}{2x^2}) dx$
negative_passages.docid: 106812
negative_passages.text: Find $\int_{0}^{\infty} \frac{\ln(x)}{1+x^2}dx$
negative_passages.docid: 149341
negative_passages.text: Help me evaluate $\int_0^1 \frac{\log(x+1)}{1+x^2} dx$
negative_passages.docid: 140386
negative_passages.text: Integrate $\int {\dfrac{x^2+\left(n-1\right)n}{\left(x\sin x+n\cos x\right)^2}}dx $
negative_passages.docid: 9390
negative_passages.text: $ \int_1^2\int_1^2 \int_1^2 \int_1^2 \frac{x_1+x_2+x_3-x_4}{x_1+x_2+x_3+x_4}dx_1dx_2dx_3dx_4 $
negative_passages.docid: 98838
negative_passages.text: How to evaluate $\int_0^1 \frac{\ln(x+1)}{x^2+1} dx$