The Laplace transform of exp(at), where a > 0, is defined only for the Laplace parameter, s > a since

• the function is exponential.
• the Laplace transform of integral of exp(at) has finite values only for s > a.
• the Laplace transform integral of exp(at) has initial values only for s > a.
• the function exp(at) is piece-wise continuous only for s > a.