Taylor series
Nonelementary antiderivatives can often be evaluated using Taylor series. Even if a function has no elementary antiderivative, its Taylor series can "always" be integrated term-by-term like a polynomial, giving the antiderivative function as a Taylor series with the same radius of convergence. However, even if the integrand has a convergent Taylor series, its sequence of coefficients often has no elementary formula and must be evaluated term by term, with the same limitation for the integral Taylor series.