  We apply a recently proposed approximation method to the evaluation of
non-Gaussian integral and anharmonic oscillator. The method makes use of the
truncated perturbation series by recasting it via the modified Laplace integral
representation. The modification of the Laplace transformation is such that the
upper limit of integration is cut off and an extra term is added for the
compensation. For the non-Gaussian integral, we find that the perturbation
series can give accurate result and the obtained approximation converges to the
exact result in the $N \to \infty$ limit ($N$ denotes the order of perturbation
expansion). In the case of anharmonic oscillator, we show that several order
result yields good approximation of the ground state energy over the entire
parameter space. The large order aspect is also investigated for the anharmonic
oscillator.
