Starting with OP's hint,
$\displaystyle \lim\limits_{n\to\infty}\int_{0}^{1}\cdots\int_{0}^{1} \left(\dfrac{x_{1}+x_{2}+\cdots+x_{n}}{n}\right)dx_{1}dx_{2}\cdots dx_{n}=\dfrac{1}{2}$,
Now, we try to show, $\displaystyle \lim\limits_{n\to\infty}\int_{0}^{1}\cdots\int_{0}^{1} \left(\dfrac{x_{1}+...
In algebra, a Bring radical or ultraradical of a complex number a is a root of the polynomial
:x^5+x+a. \,
The root is chosen so the radical of a real number is real, and the radical is a differentiable function of a in the complex plane, with a branch cut along the negative real line below −1.
George Jerrard showed that some quintic equations can be solved using radicals and Bring radicals, which had been introduced by Erland Bring. They can be used to obtain closed-form solutions of quintic equations.
Normal forms
The quintic equation is rather difficult to obtain solution...
