求不定积分∫e^(-2t)costdt
原式=∫costdt/e^(2t)=∫d(sint)/e^(2t)=sint/e^(2t)+2∫sintdt/e^(2t)
=sint/e^(2t)-2∫d(cost)/e^(2t)=sint/e^(2t)-2[cost/e^(2t)+2∫costdt/e^(2t)]
=(sint-2cost)/e^(2t)-4∫costdt/e^2t
∴5∫costdt/e^(2t)=(sint-2cost)/e^(2t)+C/5
故原式=(sint-2cost)/[5e^(2t)]+C
其中,两次用到：d[1/e^(2t)]=-2[e^(2t)dt/e^(4t)]=-2dt/e^(2t)