Definite/Indefinite Integrals Involving Non-integral Powers for Certain Trigonometric Functions Times Special Functions

Treatment of definite integrals possessing non-integral power are mainly presented. Based on definite integrals with integral power(s), non-integral cases are constructed through power series. Especially cases given by a trigonometric function are decomposed into smaller than or equal to components. Hypergeometric functions, Pochhammer functions, Gamma functions involved are easy to avoid overflow in numerical computation.