基于双元变换的一类反常积分问题的计算

Calculation of a class of abnormal integral problems based on bivariate transformation

针对一类被积函数分母含ax^(4)+bx^(2)+c的有理分式的反常积分问题,利用引入双元变换的方法,结合组合计算方法和高次有理分式化成部分有理真分式的理论,给出了积分问题的计算方法.利用所给结论,计算并证明了二类积分问题.

Aiming at the abnormal integration problem of a class of rational fractions with ax^(4)+bx^(2)+c in the denominator of the integrand function,by introducing bivariate transformation method and combining the combination calculation method with the theory of transforming high order rational fractions into partial rational true fractions,the calculation method for integration problems is proposed.Using the given conclusion,two type of integration problem is calculated and proved.