Your goal is to write a program that will print out the Laplace transform of a polynomial function with integer coefficients f(x). The Laplace transform of f(x) is defined as the integral from 0 to infinity of f(x) e^(-sx) dx.
The standard input for the polynomial function will be
If the coefficient is zero, that term is omitted. It can be taken in from any standard type of input.
This is valid input: 1+x^2-5x^4+20x^5 These aren't: 0 1+0x 1+x^1 x^0+x
You may output from any standard type of output, in any readable order. Trailing newline is permitted. No using built in evaluation functions.
Input: 1 Output: 1/s Input: 3-x Output: 3/s-1/s^2
This is code golf, so the shortest entry in bytes wins.