∫(sinx)^3(cosx)^5dx

使用简化公式∫ [(cosx) m (sinx) n] dx =

-[(cosx)^(m+1)(sinx)^(n-1)]/(m+n)

+[(n-1)/(m+n)]∫[(cosx)^m(sinx)^(n-2)]dx

原公式=-[cos 6 (x) sin？x]/(3+5)+(2/8)∫[sinxcos^5(x)]dx

=(1/4)∫[sinxcos^5(x)]dx-(1/8)sin？xcos^6(x)

=-(1/4)∫cos^5(x)d(cosx)-(1/8)sin？xcos^6(x)

=-(1/4)(1/6)cos^6(x)-(1/8)sin？xcos^6(x)+C

=-(1/24)cos^6(x)-(1/8)sin？xcos^6(x)+C

=(1/48)cos^6(x)[3cos(2x)-5]+c