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∫sin^3x Cosx/³√sinx%Cosx Dx

(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...

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...

为什么会等于0?你从哪里得到的?加减法中等价替换?

解:∵a=(cos3x/2,sin3x/2),b=(cosx/2,-sinx/2) ∴a+b=(cos3x/2,sin3x/2)+(cosx/2,-sinx/2)=(cos3x/2+cosx/2,sin3x/2-sinx/2) ∴|a+b|²=(cos3x/2+cosx/2)²+(sin3x/2-sinx/2)² =cos²(3x/2)+sin²(3x2)+cos²(x/2)...

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

∫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...

=∫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...

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