Inverse Laplace for (e)^-5t*(t)^4

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Homework Statement



Find:

Inverse Laplace for x(t)= (e)^-5t*(t)^4 using laplace table and laplace properties.

Homework Equations





The Attempt at a Solution



Well, I have been working on this problem for a few days now and cannot seem to figure it out. The two functions are not separate terms being added together so I cannot simply say

L^-1{(e)^-5t} + L^-1{(t)^4} which I originally tried. This would result in

1/s+5 + 24/s^5 which would be easy but since the two functions are being multiplied it is throwing me off and I cannot find an answer through the tables.
 
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I found a better table, this post can be deleted
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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