Find the laplace transform

Question

Answer 1

f(x) = {0 if - ∞ < x ≤ - √3; 1 + √3/3x if -√3 < x < 0, √3/3x if 0 ≤ x < √3, 0 if x ≥ √3)

L(f(x) = ∫_-√3⁰(1 + √3/3x)e^-sxdx + ∫₀^√3√3/3xe^-sxdx = - 1/s - √3/(3s²) + √3/(3s²)e^s√3- 1/se^-s√3- √3/(3s²)e^-s√3 + √3/(3s²)