用分部积分法求∫x∧2dx⼀√(x∧2-1)

2025-04-08 22:03:21
推荐回答(1个)
回答1:

令x=asint dx=acostdt t=arcsin(x/a)
原式=∫a^2cos^2tdt
=a^2/2*∫(1+cos2t)dt
=a^2/2*(t+sintcost)+C
=a^2/2*arcsin(x/a)+ax/2*(1-x^2/a^2)^(1/2)+C