1. **Problem:** Find the Laplace Transform of $$F(t) = \frac{e^{t - \cos t}}{t}$$. 2. **Recall the Laplace Transform definition:** $$\mathcal{L}\{f(t)\} = \int_0^\infty e^{-st} f(t) dt$$ 3. **Analyze the function:** The function is $$F(t) = \frac{e^t e^{-\cos t}}{t}$$. 4. **Note:** The presence of $$\frac{1}{t}$$ and the term $$e^{-\cos t}$$ makes this function non-standard and not expressible in elementary closed form Laplace transforms. 5. **Conclusion:** The Laplace transform of $$F(t)$$ does not have a simple closed form using elementary functions or standard Laplace transform tables. 6. **Alternative approach:** One might consider series expansion of $$e^{-\cos t}$$ and then attempt term-by-term Laplace transform, but this is complex and beyond standard methods. **Final answer:** The Laplace transform of $$F(t) = \frac{e^{t - \cos t}}{t}$$ cannot be expressed in a simple closed form using elementary functions.