Laplace transform using properties

phlstr
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Homework Statement


Find the laplace transform of
f(t)=(t-5)e^{-17(t-5)}u(t-5)

The Attempt at a Solution



The answer I got was \frac{e^{-5(s+17)}}{(s+17)^{2}}.
I thought I finally understood the process, but when I plugged it into wolfram alpha, the answer I got was different...

http://www.wolframalpha.com/input/?i=laplace+transform+of+((t-5)e^(-17(t-5)))*theta(t-5)

Shouldn't the "s" in the exponent be "s+17" or is my understanding really wrong??
 
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Wolfram Alpha's answer is the correct one.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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