  In this paper we extend the Zeta function regularization technique, which
gives a meaningful solution to divergent power series, in order to assign
finite values to divergent integral of certain transcendental functions $f(x)$.
The functions are assumed to be analytical and hence they have a convergent
Maclaurin series with infinity radius of convergence. Using Maclaurin series
and binomial expansion, we equivalently convert the divergent integral to an
infinite series in terms of Riemann zeta function. It is shown that the
infinite series is convergent under a certain condition and consequently the
solution 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 of
this Zeta regularization technique is that it does not not require introducing
any cut-off function to calculate such divergent integrals. This formula is
applied to calculate the divergent integral of several common transcendental
functions.
