Check my work on laplace inverse #2 I hope that am on the right path

Max64

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S2 + 10π + 24π2 = (S + 5π)2 - π2 = (S + 6π)(S + 4π)

so

\(\displaystyle \dfrac{\pi}{S^2 + 10\pi + 24\pi^2}\)

\(\displaystyle = \dfrac{1}{2}\left(\dfrac{1}{S + 4\pi} - \dfrac{1}{S + 6\pi}\right)\)

Now continue....
 
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