渭南师范学院学报：综合版
渭南師範學院學報：綜閤版
위남사범학원학보：종합판
Journal of Weinan Teachers College
2012年
12期
13-16
,共4页
双曲函数%双曲函数有理式%不定积分%万能代换%指数代换
雙麯函數%雙麯函數有理式%不定積分%萬能代換%指數代換
쌍곡함수%쌍곡함수유리식%불정적분%만능대환%지수대환
hyperbolic function%hyperbolic function rational formula%indefinite integral%universal substitution%exponential substitution
在介绍双曲函数的概念及双曲函数的有关恒等式、微分和积分公式的基础上，探讨了双曲函数有理式的可积性问题．通过万能或指数代换，得到并证明了双曲函数有理式的原函数都是初等函数这一重要结论．进一步给出并证明了几个常用的递推公式，通过实例说明了如何求双曲函数有理式的不定积分．
在介紹雙麯函數的概唸及雙麯函數的有關恆等式、微分和積分公式的基礎上，探討瞭雙麯函數有理式的可積性問題．通過萬能或指數代換，得到併證明瞭雙麯函數有理式的原函數都是初等函數這一重要結論．進一步給齣併證明瞭幾箇常用的遞推公式，通過實例說明瞭如何求雙麯函數有理式的不定積分．
재개소쌍곡함수적개념급쌍곡함수적유관항등식、미분화적분공식적기출상，탐토료쌍곡함수유리식적가적성문제．통과만능혹지수대환，득도병증명료쌍곡함수유리식적원함수도시초등함수저일중요결론．진일보급출병증명료궤개상용적체추공식，통과실례설명료여하구쌍곡함수유리식적불정적분．
Based on the hyperbolic function concept, and identity, differential and integral formulas of the hyperbolic function, the paper discusses the problems about the integrability of the hyperbolic function rational formula. Through universal or exponential substitution, the paper obtains and proves that the function which belongs to the hyperbolic function rational formula is an elementary function. Furthermore, the paper gives and proves several commonly used recursive formula. Hence, the paper takes examples to il- lustrate how to seek the hyperbola function rational formula of definite integral
