∫sin^nxdx用分部积分法!

题目

∫sin^nxdx用分部积分法!

答案

原式=∫sin^(n-1)xsinxdx=-∫sin^(n-1)xdcosx=-cosxsin^(n-1)x+∫cosxdsin^(n-1)x=-cosxsin^(n-1)x+∫(n-1)sin^(n-2)xcos²xdx=-cosxsin^(n-1)x+(n-1)∫[sin^(n-2)x-sin^nx]dx=-cosxsin^(n-1)x+(n-1)∫sin^(n-2)...