多少求导等于sinx的四次方,

题目

多少求导等于sinx的四次方,

答案

(1)先求 S(sin2x)^2dx=x/2-(1/4)sina2xcos2x
S(sin2x)^2dx=-(1/2)Ssin2xdcos2x
=-(1/2){ sin2xcos2x-2Scos2xcos2xdx}
=-(1/2){sin2xcos2x-2S(1-(sinx)^2)dx}
=-(1/2)sin2xcos2x+S(1-(sinx)^2)dx
=-(1/2)sin2xcos2x+x-S((sinx)^2)dx
S(sin2x)^2dx=-(1/4)sin2xcos2x+(1/2)x
(2)S(sinx)^4dx=-S(sinx)^3dcosx
=-(sinx)^3 cosx+3Scos^2xsin^2xdx
=-(sinx)^3 cosx+(3/4)S4cos^2xsin^2xdx
=-(sinx)^3 cosx+(3/4)Ssin^2 2xdx
=-(sinx)^3 cosx+(3/4)( x/2-(1/4)sina2xcos2x)
下面自己整理吧