∫sint*sinwtdt怎么求积分?还有∫cost*coswtdt?

用积化和差公式：sinxsiny=(1/2)[cos[(x-y)-cos(x+y)],cosxcosy=(1/2)[cos(x+y)+cos(x-y)]
∫sint*sinωt dt
= (1/2)∫cos(t-ωt) dt - (1/2)∫cos(t+ωt) dt
= (1/2)∫cos(1-ω)t dt - (1/2)∫cos(1+ω)t dt
= (1/2)/(1-ω)∫cos(1-ω)t d(1-ω)t - (1/2)/(1+ω)∫cos(1+ω)t d(1+ω)t
= 1/[2(1-ω)] * sin[(1-ω)t] - 1/[2(1+ω)] * sin[(1+ω)t] + C
∫cost*cosωt dt
= (1/2)∫cos(t+ωt) dt + (1/2)∫cos(t-ωt) dr
= (1/2)/(1+ω)∫cos(1+ω)t d(1+ω)t + (1/2)/(1-ω)∫cos(1-ω)t d(1-ω)t
= 1/[2(1+ω)] * sin[(1+ω)t] + 1/[2(1-ω)] * sin[(1-ω)t] + C