Laplace Transforms Property

Question

Please see image. I'm confused by how the went about to get d[exp(-st)] in the second line

Thanks Laplace Transform

Answer 1

For $s$ held constant,

$$ e^{-st} \,\mathrm{d}t = -\frac{1}{s} \,\mathrm{d}(e^{-st}). $$