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In this paper we extend the Zeta function regularization technique, whichgives a meaningful solution to divergent power series, in order to assignfinite values to divergent integral of certain transcendental functions $f(x)$.The functions are assumed to be analytical and hence they have a convergentMaclaurin series with infinity radius of convergence. Using Maclaurin seriesand binomial expansion, we equivalently convert the divergent integral to aninfinite series in terms of Riemann zeta function. It is shown that theinfinite series is convergent under a certain condition and consequently thesolution of the divergent integral becomes $\int_0^{\infty} f(x) dx =\sum_{k=0}^{\infty} \frac{(-1)^{k+1}}{(k+2)!} f^{(k)}(0)$. The advantage ofthis Zeta regularization technique is that it does not not require introducingany cut-off function to calculate such divergent integrals. This formula isapplied to calculate the divergent integral of several common transcendentalfunctions.

Divergent Integrals of Certain Analytical Functions In the Sense of Zeta Regularization