Set of positive integers

Find all possible integers $n$ such that $\sqrt{n + 2} + \sqrt{n + \sqrt{n + 2}}$ is an integer.

Wish to evaluate $\int_{0}^{1}\frac{x^4-3x^2+2x}{\sin(\pi x)} dx$

Relationship between a determinant and the roots of a cubic equation

Combinatorial Proof of $3^n - 2^n = \sum_{i=0}^{n-1}2^i3^{n-1-i}$

Question for finding bound for $f'(z)$[CSIR-December 2011]

maximum and minimum value of $\frac{x^2+y^2}{x^2+xy+4y^2}$

Minimum of a sum of positive functions is the sum of the minimums of the functions

Compute $\int_0^\infty \frac{\operatorname{Li}_3(x)}{1+x^2}\ dx$

Integrate without expansion?

Given $51$ natural numbers whose sum is $100$, show that it is possible to split them to $2$ sets such that each of them is $50$.

Image of $T:E \rightarrow \alpha E + (1-\alpha) E$ where $\alpha>1$.

Find $\int_0^1 \frac{\ln^2x\arctan x}{x(1+x^2)}\ dx$

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