例12求∫ sin xcos xdx 解「im2 xcos xdx=sm2 xcos'xcos xdx sin2x1-sin x ∫sm小-2 sinx+sinx)smx sin2x-2sin4x +sinx Hsin sin'x--sin'x+-sin x+C 5sin cos . 2 5  求 x xdx  x xdx 2 5 sin cos  = sin xcos xcos xdx 2 4 ( )  = sin x 1− sin x sin x 2 2 2 d ( )  = sin x 1− 2sin x + sin x sin x 2 2 4 d ( )  = sin x − 2sin x + sin x sin x 2 4 6 d sin . 7 1 sin 5 2 sin 3 1 3 5 7 = x − x + x + C 例12 解