Solve Laplace Transform of e^-te^tcost

[Turion]

Homework Statement

$$L\{ { e }^{ -t }*{ e }^{ t }cost\}$$

Homework Equations

The Attempt at a Solution

$$L\{ { e }^{ -t }*{ e }^{ t }cost\} \\ =L\{ \int _{ 0 }^{ t }{ { e }^{ -\tau }{ e }^{ t-\tau }cos(t-\tau )d\tau } \} \\ =\frac { L\{ { e }^{ t }cost\} }{ s } \\ =\frac { s-1 }{ s[{ (s-1) }^{ 2 }+1] }$$

 

[szynkasz]

Unfortunately it isn't correct. For convolution we have:

$L\{f*g\}=L\{f\}\cdot L\{g\}$