Inverse Laplace transform of F(s)=(e^(-4s)-e^(-5s))/s^6

[Daniel_Feldman]

I need to find the inverse Laplace transform of

F(s)=(e^(-4s)-e^(-5s))/s^6

I'm not sure how to convert it to one of the "common" laplace transforms that are in those tables. Any help would be appreciated.

 

[galactus]

Hey Dan:

I have a Laplace solver in my TI. I entered in yours and it gave me a long answer.

\(\displaystyle \frac{u(t-4)t^{5}}{120}-\frac{u(t-4)t^{4}}{6}+\frac{4u(t-4)t^{3}}{3}-\frac{16u(t-4)t^{2}}{3}+\frac{32u(t-4)t}{3}-\frac{128u(t-4)}{15}-\frac{u(t-5)t^{5}}{120}+\frac{5u(t-5)t^{4}}{24}-\frac{25u(t-5)t^{3}}{12}+\frac{125u(t-5)t^{2}}{12}-\frac{625u(t-5)t}{24}+\frac{625u(t-5)}{24}\)

That's rather icky. One would think it would be easier than that.

 

[tkhunny]

That 6 dictates the number of terms - six for each exponential in the numerator.