1/((x^2-1)^(1/2))的原函数怎么算?

Question

1/((x^2-1)^(1/2))的原函数怎么算?

Answer 1

令x=sec t,则dx=sec t*tan tdt
1/((x^2-1)^(1/2))dx=sec tdt=sec(sec t+tan t)*sec(sec t+tan t)^(-1) dt=sec(sec t+tan t)^(-1)d(sec t+tan t)=ln|sec t+tan t|+C