{sinlnxdx令t=lnx{sintdt=tsint-{costdt=tsint-(tcost+{sintdt)=1
1个回答

{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.