Finding the Laplace transform of cos²at

[Mdhiggenz]

Homework Statement

L[cos²at]

I know that L[cost] = s/(s²+b^s)

I know that cos²at can also be written as 1/2(1+cos2at)

and so I then got the L[1/2]+1/2L[cos2at)]

Which gave me s/(s²+(2a)²)

However this is not correct, there was a + 2at term on the numerator as well.

Homework Equations

The Attempt at a Solution

 

[rock.freak667]

L[tⁿ] = n!/sⁿ⁺¹

For L[1/2], n= 0 so you should get 1/2s as that transform.