Given a polynominal, each coefficient of which is rational, with one argument, output an expression with only `1`, definite integral, and variables, that equals to it. E.g. -*x*<sup>2</sup> can be expressed as ∫<sub>*x*</sub><sup>∫<sub>1</sub><sup>1</sup>1d*t*</sup>*x*d*u*.

<code>E := 1 | var | ∫<sub>E</sub><sup>E</sup>Edvar</code>

Reasonable input/output method allowed

Samples:

[![\Large 1=1\\ \Large x=x\\ \Large 0 = \int_1^1 1\text dt\\ \Large 2 = \int_{\int_1^{\int_1^1 1\text dv} 1\text du}^1 1\text dt\\ \Large x^2=\int_{\int_1^1 1\text dt}^x x\text dv\\ \Large \frac 12=\int_{\int_1^1 1\text dt}^1 v\text dv][1]][1]

Your score will be the your code length multiply how many symbol `∫` used on the test cases. You should be able to score your program. Lowest score win.

Test cases:

    4/381*x^2+49/8*x^3-17/6
    311/59*x^2-92/9*x^3-7/15*x
    333/29*x^3+475/96*x^8

  [1]: https://latex.codecogs.com/gif.download?%5C%5C%20%5CLarge%201%3D1%5C%5C%20%5CLarge%20x%3Dx%5C%5C%20%5CLarge%200%20%3D%20%5Cint_1%5E1%201%5Ctext%20dt%5C%5C%20%5CLarge%202%20%3D%20%5Cint_%7B%5Cint_1%5E%7B%5Cint_1%5E1%201%5Ctext%20dv%7D%201%5Ctext%20du%7D%5E1%201%5Ctext%20dt%5C%5C%20%5CLarge%20x%5E2%3D%5Cint_%7B%5Cint_1%5E1%201%5Ctext%20dt%7D%5Ex%20x%5Ctext%20dv%5C%5C%20%5CLarge%20%5Cfrac%2012%3D%5Cint_%7B%5Cint_1%5E1%201%5Ctext%20dt%7D%5E1%20v%5Ctext%20dv