Question

这道不定积分问题求解，需要详细过程，谢谢

Answer 1

=∫sintde^t
=sinte^t-∫e^tdsint
=sinte^t-∫costde^t
=sinte^t-coste^t+∫e^tdcost
=sinte^t-coste^t-∫sintde^t
=e^t(sint-cost)/2+C
=x(sinlnx-coslnx)/2+C

追问

那个e∧t是咋来的？

追答

明显的换元lnx=t，x=e^t