【摘要】 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.更多还原

【Abstract】 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 illustrate how to seek the hyperbola function rational formula of definite integral更多还原