- #1

- 143

- 2

## Homework Statement

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

## Homework Equations

## The Attempt at a Solution

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