A Simple Method for Computing Some Pseudo-Elliptic Integrals in Terms of Elementary Functions
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We introduce a method for computing some pseudo-elliptic integrals in terms of elementary functions. The method is simple and fast in comparison to the algebraic case of the Risch-Trager-Bronstein algorithm. This method can quickly solve many pseudo-elliptic integrals, which other well-known computer algebra systems either fail, return an answer in terms of special functions, or require more than 20 seconds of computing time. Randomised tests showed our method solved 73.4 of the Risch-Trager-Bronstein algorithm. Unlike the symbolic integration algorithms of Risch, Davenport, Trager, Bronstein and Miller; our method is not a decision process. The implementation of this method is less than 200 lines of Mathematica code and can be easily ported to other CAS that can solve systems of polynomial equations.
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