sin2xsin3x积化和差

万会蚀3348f(x)=sinxsin2xsin3x 求其n阶导数 -
华江戴15084844383 ______ lim(tanx-sinx)/sin^3x =limsinx(1/cosx-1)/sin^3x =lim(1-cosx)/[sin^2x*cosx] =lim2(sinx/2)^2/[4(sinx/2)^2(cosx/2)^2*cosx] =lim1/[2(cosx/2)^2*cosx] 当x→2π时 cosx/2→ -1 cosx→ 1 原极限=1/2

万会蚀3348求一道积分题,sinxsin2xsin3xdx的积分 -
华江戴15084844383 ______[答案] sinxsin2xsin3x =1/2(cos2x-cos4x)sin2x =1/4sin4x-1/4(sin6x-sin2x) =1/4(sin4x-sin6x+sin2x) 所以∫sinxsin2xsin3xdx =1/4∫(sin4x-sin6x+sin2x)dx =1/4(-1/4*cos4x+1/6*cos6x-1/2*cos2x)+C =1/24cos6x-1/16cos4x-1/8cos2x+C

万会蚀3348求助,对sinxsin2xsin3x 求积分 -
华江戴15084844383 ______ ∫[sinxsin(3x)]dx =∫½[cos(x-3x)-cos(x+3x)]dx =½∫[cos(-2x)-cos(4x)]dx =½∫[cos(2x)-cos(4x)]dx =½∫cos(2x)dx -½∫cos(4x)dx =¼∫cos(2x)d(2x)-U憨旦封秆莩飞凤时脯江39;∫cos(4x)d(4x) =-¼sin(2x)+⅛sin(4x)+C 提示:先对

万会蚀3348求sinxsin2xsin3x的不定积分,要具体步骤 -
华江戴15084844383 ______ ∫sinxsin2xsin3xdx =∫sinx * (1/2)(cosx-cos5x)dx =(1/2)∫sinxcosxdx - (1/2)∫sinxcos5xdx =(1/2)∫sinxdsinx - (1/4)∫(sinx6x-sin4x)dx =(1/2)(sin²/2) - (1/4)(-1/6)cos6x + (1/4)(-1/4)cos4x + C = (1/4)sin²x + (1/24)cos6x - (1/16)cos4x + C

万会蚀3348还有一题sin2x/(sinx的平方+3)的不定积分 -
华江戴15084844383 ______ ∫ sin2x/(sin²x + 3) dx= ∫ 2sinxcosx/(sin²x + 3) dx= ∫ 2sinx/(sin²x + 3) dsinx= ∫ 1/(sin²x + 3) dsin²x= ∫ 1/(sin²x + 3) d(sin²x + 3)= ln(sin²x + 3) + constant

万会蚀3348sin²2xsin3x的积分 -
华江戴15084844383 ______ sin^2xsin3x=0.5(1-cos4x)sin3x=0.5 sin3x-0.5sin3xcos4x=0.5sin3x-0.25 (sin7x-sinx) I= -1/6 cos3x + 1/28 cos7x- 1/4 cosx +C

万会蚀3348∫sin2x dcos3x怎么解啊 告诉方法就可以不用打 -
华江戴15084844383 ______ ∫sin2x dcos3x =-∫3sin2x sin3xdx 然后sin2xsin3x用积化和差分开再积分就可以了

万会蚀33482sinxsin3x该如何化简啊 -
华江戴15084844383 ______[答案] 2sinxsin3x=cos(3x-x)-cos(x+3x)=cos2x-cos4x 你要的是和差化积吧

万会蚀3348sin2xcos3x= - 1 - cos2xsin3x -
华江戴15084844383 ______ sin(5x)=-1 x=2k∏-∏/2

万会蚀3348cos2xsin3x 的2011阶导数 -
华江戴15084844383 ______[答案] 由积化和差公式,得: cos2xsin3x=[sin(3x+2x)+sin(3x-2x)]/2=(1/2)·(sin5x+sinx) (sin5x)'=5cos5x,(sin5x)＂=-25sin5x,…,sin5x的2011阶导数=-5^2011·cos5x (sinx)'=cosx,(sinx)＂=-sinx,…,sinx的2011阶导数=-cosx ∴cos2xsin3x 的2011阶导数=-(...