例4计算sin3x-sin5xdkx 解∵f(x)=in3x- sin x coS sinx sin'x-sinsxdx =l cos xsinx 2 de 3 ∫cosx(sinx)2 dx-f cosxsin.xide a(sin x)id sin.x-f(sin inx2dsinx 5 inx sIn x 5例4 计算 sin sin . 0 3 5   x − xdx 解 f x x x 3 5  ( ) = sin − sin ( )2 3 = cos x sin x    − 0 3 5 sin x sin xdx ( )   = 0 2 3 cos x sin x dx ( )   = 2 0 2 3 cos x sin x dx ( )  −   2 2 3 cos x sin x dx ( )   = 2 0 2 3 sin x d sin x ( )   −  2 2 3 sin x d sin x ( ) 2 0 2 5 sin 5 2  = x ( )   − 2 2 5 sin 5 2 x . 5 4 =