Find Real Values of K in Laplace Transform Homework

[Precursor]

Homework Statement
If f(t)=K + 2cost and F(s) = L{f(t)}, find all the real values of K such that \int_{1}^{2}F(s)ds = 2ln5


The attempt at a solution
So L{f(t)} = L{K} + L{2cost} = (K/s) + [2/(s² + 1)]

So \int_{1}^{2}\frac{K}{s}ds + \int_{1}^{2}\frac{2s}{s^{s}+1}ds = 2ln5

After integration(I used integration by substitution for the second integral) and simplification, I get K(ln2) + ln(2) = 2ln(5)

Finally, I get K = [ln 25 - ln2]/ln2

Is this correct?

 

[timthereaper]

After integration(I used integration by substitution for the second integral) and simplification, I get K(ln2) + ln(2) = 2ln(5)

The second term in your equation is supposed to be ln(5). Using your method, I get K = 1+ln(5)/ln(2) or ln(10)/ln(2). But I don't see a problem with your method.

 

[vela]

Just doing this in my head, but I think the second integral evaluates to log(5/2).

 

[Precursor]

I forgot to change the limits of integration when I used the method of substitution.