{sinlnxdx
令t=lnx x=e的t次方(et),dx=etdt.
{sinlnxdx={sint*etdt={sintdet=etsint-{cost*etdt=et*sint-(cost*et+{sint*etdt)
所以{sint*etdt=et*sint-(cost*et+{sint*etdt)
移项得到{sint*etdt==0.5*(et*sint-cost*et)=(1/2)*et(sint-cost)
带入t=lnx就得到{sinlnxdx=(1/2)*x(sinlnx-coslnx)
你错就错在dx的计算上.