设t=lnx,
x=e^t,
dx=e^tdt,sin(lnx)=∫sint*e^tdt=sint*e^t-∫cost*e^tdt=sint*e^t-[e^tcost+∫sint*e^tdt]
=sint*e^t-e^tcost-∫sint*e^tdt
∫sint*e^tdt=e^t(sint-cost)/2+C,原式=x[sin(lnx)-cos(lnx)]/2+C.
求sin（lnx）的不定积分 要详细过成功 注意这是复合函数.
设t=lnx,
x=e^t,
dx=e^tdt,sin(lnx)=∫sint*e^tdt=sint*e^t-∫cost*e^tdt=sint*e^t-[e^tcost+∫sint*e^tdt]
=sint*e^t-e^tcost-∫sint*e^tdt
∫sint*e^tdt=e^t(sint-cost)/2+C,原式=x[sin(lnx)-cos(lnx)]/2+C.