  In this paper, we obtain the analytical solutions of Laplace transforms based
some novel integrals with suitable convergence conditions, by using
hypergeometric approach (some algebraic properties of Pochhammer symbol and
classical summation theorems of hypergeometric series ${}_{2}F_{1}(1)$,
${}_{2}F_{1}(-1)$ , ${}_{4}F_{3}(-1)$) . Also, we obtain the Laplace transforms
of arbitrary powers of some finite series containing hyperbolic sine and cosine
functions having different arguments, in terms of hypergeometric and Beta
functions. Moreover, Laplace transforms of even and odd positive integral
powers of sine and cosine functions with different arguments, and their
combinations of the product (taking two, three, four functions at a time), are
obtained. In addition, some special cases are yield from the main results.
