确定有理函数积分中待定系数的方法研究

Research on the Approaches to Fixing the Undetermined Coefficient in integral of Rational Function

有理函数的积分是不定积分中的一种重要类型,在大学数学中占有重要地位.将有理函数分解为部分分式的难点就是确定部分分式中的待定系数.本文系统地介绍了确定有理函数积分中待定系数的各种方法,综合运用这些方法,能快速、有效地将有理函数分解成部分分式,从而可方便地解决一类有理函数的积分问题.

The integral of rational functions,which plays an important role in college mathematics,is a major type of indefinite integrals. The difficulty in decomposing rational function into partial fraction is to fix the undetermined coefficient in partial fraction. The approaches to fixing undetermined coefficient introduced in present teaching materials are partial and quite complicated, therefore, it is important to research for better approaches. This thesis systematically introduces several approaches, some of which are derived from many years of teaching experience. By using these approaches an integrate problems can be solved quickly and efficiently.