令x=asect,dx=sect tant dt
åå¼=â«atant*d(asect)
=a^2â«tant sect tant dt (1)
=a^2â«tant d sec t
=a^2tant sect -a^2â«sect sec^2 t dt
=a^2tant sect -a^2â« sect(tan^2 t+1) dt
=a^2tant sect -a^2â«sect dt -a^2â«tant sect tant dt (2)
èç«(1),(2)
æ以
a^2â«tant sect tant dt=a^2/2[tant sect -â«sect dt]
=a^2/2[tant sect- ln|sect+tan t| ]+C
=a^2/2*xâ(x²-a²)-a^2/2ln|x+â(x²-a²)|+c
温馨提示:答案为网友推荐,仅供参考