query: Evalution of a function where $t = x + \frac{1}{x}$
positive_passages.docid: 44233
positive_passages.text: How to prove this inequality $ x + \frac{1}{x} \geq 2 $
negative_passages.docid: 32312
negative_passages.text: Evaluating the integral $\int \frac{x^2+x}{(e^x+x+1)^2}dx$
negative_passages.docid: 76474
negative_passages.text: How to make a function that evaluates an expression?
negative_passages.docid: 129052
negative_passages.text: Find all functions satisfying $\frac{1}{f(a)}+ \frac{1}{f(b)} = \frac{1}{f(c)} $ whenever $\frac{1}{a}+ \frac{1}{b} = \frac{1}{c} $
negative_passages.docid: 69978
negative_passages.text: Evaluating $\int_1^\infty \frac{1}{x(x^2+1)}\ dx$
negative_passages.docid: 6382
negative_passages.text: Showing $\frac{x}{1+x}0$ using the mean value theorem
negative_passages.docid: 53719
negative_passages.text: Evaluate $\lim_{x \to 0} \left(\frac{1}{\ln(1+x)} + \frac{1}{\ln(1-x)}\right)$
negative_passages.docid: 1582
negative_passages.text: $f(x+1)-f(x)$ converges $\Rightarrow\frac{f(x)}x$ converges
negative_passages.docid: 60831
negative_passages.text: Need hint for $\lim_{x\to 0} \frac{(x+1)^\frac{1}{x}-e}{x}$
negative_passages.docid: 153867
negative_passages.text: Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$
negative_passages.docid: 103310
negative_passages.text: Evaluation of the following expression
negative_passages.docid: 99690
negative_passages.text: Find the interval over which this function is greater than 1
negative_passages.docid: 131310
negative_passages.text: Evaluating $\dfrac{1}{\sin(2x)} + \dfrac{1}{\sin(4x)} + \dfrac{1}{\sin(8x)} + \dfrac{1}{\sin(16x)}$
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: 131847
negative_passages.text: $\frac{(x-1)(x+1)}{ (x+1)} \rightarrow (x-1)$ Domain Change
negative_passages.docid: 81057
negative_passages.text: Evaluation of $\int_{\frac{1}{e}}^{\tan x}\frac{t}{1+t^2}dt+\int_{\frac{1}{e}}^{\cot x}\frac{1}{t(1+t^2)}dt$
negative_passages.docid: 43509
negative_passages.text: Evaluating $\sum_{n=1}^{\infty}\frac{(n-1)!}{\prod_{r=1}^{n}(x+r)}$ for $x\in\mathbb{R}^{+}$