# Thread: Laplace Transform of Integral

1. ## Laplace Transform of Integral

Find f(t) if L(f) = 5/[s**2 - 5s]

From this, I can see components of cosh(SQRT(5)t), but the answer in the back of the book is cosh(SQRT(5)t) - 1.

Just not quite seeing how to get there. If anyone can provide guidance (not necessarily the full answer), it will be much appreciated.

2. Originally Posted by dsprice
Find f(t) if L(f) = 5/[s**2 - 5s]

From this, I can see components of cosh(SQRT(5)t), but the answer in the back of the book is cosh(SQRT(5)t) - 1.

Just not quite seeing how to get there. If anyone can provide guidance (not necessarily the full answer), it will be much appreciated.
$f(t) = 5 L^{-1} \left[ \frac{1}{s(s - 5)} \right] = 5 L^{-1} \left[ \frac{A}{s} + \frac{B}{s - 5} \right] = 5 (A + B e^{5t})$

where you should be able to get the constants A and B arising from the partial fraction decomposition.

3. I now see where I messed up...right at the beginning.

Instead of "Find f(t) if L(f) = 5/[s**2 - 5s]"...

...It should have been "Find f(t) if L(f) = 5/[s**3 - 5s]"

I now understand how to work it out.