求不定积分∫(sinx⼀1+cosx)dx

2024-11-16 17:48:52
推荐回答(2个)
回答(1):

∫(sinx/1+cosx)dx =-∫1/1+cosx d (cosx)
=-∫1/1+cosx d (cosx+1)
=-In|1+cosx|+c

回答(2):

∫(sinx)/(1+cosx)dx
=∫(2sin(x/2)cos(x/2)/2cos(x/2)^2)dx
=∫tan(x/2)dx
=2∫tan(x/2)d(x/2)
=-2∫cos(x/2)d(cos(x/2))
=-2ln|cos(x/2)|+C