求不定积分sin根号下x

题目

求不定积分sin根号下x

答案

设√x=t,x=t^2,dx=2tdt,
原式=∫sint*2tdt=2∫t*sintdt
=2∫td(-cost)
=-2tcost+2∫costdt
=-2tcost+2sint+C
=-2√xcos√x+2sin√x+C.