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We propose a general method for constructing the semi-analytical solution of the inverse Laplace transform, realized through the powerful exponential approximation invented by Wang et al. in 1993. Bearing their credits, this method inherits all the merits such as analytical expression, avoiding free parameters, simple calculation with high accuracy, and the availability of error estimation. Illustrating calculations indicate the potential applications to the vast problems in the fields of mathematical physics as well as engineering and medicine.