A one-sided (singly infinite) Laplace transform,
This is the most common variety of Laplace transform and it what is usually meant by "the" Laplace transform. The unilateral Laplace transform is implemented in the Wolfram Language as LaplaceTransform[expr, t, s].
More things to try:
Weisstein, Eric W. "Unilateral Laplace Transform." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/UnilateralLaplaceTransform.html