# Integral Transform problem

1. Apr 15, 2007

### chickens

1. The problem statement, all variables and given/known data

L[cos(at)cosh(at)] = ?

2. Relevant equations

L[cos(at)] = s/(s^2 + w^2)

3. The attempt at a solution

I'm able to get the solution given that is (s^3)/(s^4 + 4a^4)

The question requested to use first shift property. So I used cosh(at) = 1/2[e^at + e^(-at)]

but now I'm trying to use another method.

if you use euler's rule, you can also get cos(at) = cosh(at) = 1/2[e^at + e^(-at)]

then simply multiply them and get L[e^2at + 2 + e^(-2at)] but I dont seem to get the same solution as above, any ideas?

2. Apr 15, 2007

### HallsofIvy

Staff Emeritus
No, Euler's rule does NOT say cos(at)= cosh(at)!
You may be thinking of
$$cos(at)= \frac{e^{iat}+ e^{-iat}}{2}$$
Note the "i" s in that!