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∫sin^3x Cosx/³√sinx%Cosx Dx

∫x²sin³xdx=1/4∫x²(3sinx-sin3x)dx =3/4∫x²sinxdx-1/4∫x²sin3xdx =-3/4∫x²dcosx+1/12∫x²dcos3x =-3/4x²cosx+3/4∫cosxdx²+1/12x²cos3x-1/12∫cos3xdx² =-3/4x²cosx+3/2∫xcosxdx+1/12...

解: sin³x-cos³x =(sinx-cosx)(sin²x+sinxcosx+cos²x) =(sinx-cosx)(1+sinxcosx) =sinx+sin²xcosx-cosx-sinxcos²x =sinx-cosx+½sinxsin2x-½cosxsin2x =sinx-cosx-¼(cos3x-cosx)-¼(sin3x+sin...

sin3x=sin(x+2x)=sinxcos2x+cosxsin2x=sinx(1-2sin²x)+cosx(2sinxcosx) =sinx-2sin³x+2sinxcos²x =sinx-2sin³x+2sinx(1-sin²x) =3sinx-4sin³x 同理可得:cos3x=4cos³x-3cosx ∴原式=(4sinx-4sin³x)/(4c...

(sinx)^6(cosx)^4 =sin²x(sin²xcos²x)² =¼sin²xsin²(2x) =(¼)(¼)[cos(2x-x)-cos(2x+x)]² =(1/16)[cosx-cos(3x)]² =(1/16)[cos²x-2cosxcos(3x)+cos²(3x)] =(1/16)cos²x-...

∫x²sin³xdx=1/4∫x²(3sinx-sin3x)dx =3/4∫x²sinxdx-1/4∫x²sin3xdx =-3/4∫x²dcosx+1/12∫x²dcos3x =-3/4x²cosx+3/4∫cosxdx²+1/12x²cos3x-1/12∫cos3xdx² =-3/4x²cosx+3/2∫xcosxdx+1/12...

答: lim(x→0) (cosx-cos3x)/x² =lim(x→0) 2sin(2x)sinx /x² =lim(x→0) 4sin²xcosx/x² =4 lim(x→0) (cosx-cos3x)/x² =lim(x→0) (-sinx+3sin3x)/(2x) =lim(x→0) (-cosx+9cos3x)/2 =(-1+9)/2 =4 可以用,没有问题

=∫1/[2sin(x/2)cos(x/2)] dx=∫1/[sin(...sinx=[1-(1-2sin^2(x/2))]/sinx=(1-cosx)...求解∫csc³xdx的不定积分 15 不定积分求解...

向量a=(cos3x/2,sin3x/2),向量b=(cosx/2,-sinx/2), ∴ |a|=|b|=1 a●b=cos3x/2cosx/2-sin3x/2sinx/2 =cos2x ∴|a+b|²=|a|²+|b|²+2a●b =1+1+2cos2x=2+2cos2x |a+b|²最大值为4,最小值为0 ∴|a+b|的取值范围是[0,2] 法2: 向量a=(...

2、求下列函数的导数 (1)y'=(sin²x)'-(cos2x)'=2sinx•(sinx)'-(-sin2x)•(2x)'=2sinxcosx+2sin2x=3sin2x (2)y'=...

lim(1+sinx)^(2/x)=e^2 lim1-cos2x/(sin^2)3x=1/18 lim(x-1)(sin1/x-1)=1

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