Method of Moment Estimator on function

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For an assignment i need to calculate an estimator using the method of moments, assuming a> 0. $$f(x)=x/(2*a)*e^{(|x|/a)}$$
I calculated $E(X)$ and E($X^2)$, but if a is a positive number the Integral is $\infty$
What should I do in this situation or is this just the answer, that there is no estimator?