1除以cos3次方的不定积分

柴昆侄4026cos^3(x) dx的不定积分 -
古茜春18495724521 ______[答案] 一楼的解答,舍近求远. ∫cos³xdx =∫cos²xcosxdx =∫cos²xdsinx =∫(1-sin²x)dsinx =∫dsinx - ∫sin²xdsinx = sinx - (1/3)sin³x + c

柴昆侄4026求x^2 cos^3(x)的积分 -
古茜春18495724521 ______[答案] 求不定积分:∫x² cos³xdx 由于cos³x=(1/4)(3cosx+cos3x),故: 原式=∫x²[(1/4)(3cosx+cos3x)dx=(1/4)(3∫x²cosxdx+∫x²cos3xdx) =(1/4)[3∫x²dsinx+(1/3)∫x²dsin3x]=(1/4)[3(x²sinx-2∫xsinxdx)+(1/3)(x²sin3x-2∫xsin3xdx)] =(1/4){3(x²sinx+2∫...

柴昆侄4026化简:sin3α,cos3α(分别用sinα,cosα表示) -
古茜春18495724521 ______[答案] 三倍角公式 三倍角的正弦、余弦和正切公式 sin3α=3sinα-4sin^3(α) cos3α=4cos^3(α)-3cosα tan3α=[3tanα-tan^3(α)]/[1-3tan^2(α)] [编辑本段]三倍角公式推导 附推导: tan3α=sin3α/cos3α =(sin2αcosα+cos2αsinα)/(cos2αcosα-sin2αsinα) =(2sinαcos^2(α)+...

柴昆侄4026cos的六次方的不定积分怎么求解!那它在0到2/π的定积分是多少? -
古茜春18495724521 ______[答案] so easy let me teach you. cos⁶x = (cos²x)³ = [(1 + cos2x)/2]³ = (1/8)(1 + cos2x)³ = (1/8)(1 + 3cos2x + 3cos²2x + cos³... 5x/16 + (15/32)(1/2)sin2x + (3/16)(1/4)sin4x + (1/32)(1/6)sin6x + C = 5x/16 + (15/64)sin2x + (3/64)sin4x + (1/192)sin6x + C 楼...

柴昆侄4026∫x^2cos3xdx的不定积分是多少 -
古茜春18495724521 ______[答案] 用两次分步积分法 ∫x^2cos3xdx =1/3∫x^2dsin3x =1/3x^2sin3c-2/3∫xsin3xdx =1/3x^2sin3c+2/3∫xdcos3x =1/3x^2sin3c+2/3xcos3x-2/3∫cos3xdx =1/3x^2sin3c+2/3xcos3x-2/9sin3x+C

柴昆侄4026cos3xsinxdx的不定积分是多少注意cos3是cos的三次 -
古茜春18495724521 ______[答案] ∫cos³xsinxdx =-∫cos³xdcosx =-1/4(cosx)的4次方+c

柴昆侄4026lim[(cos x)的(1除以x平方) 次方],x 趋近于0时原式等于多少? -
古茜春18495724521 ______[答案] lim[(cos x)^(1/x^2) ], =lim[1-2sin^2(x/2)]^(1/x^2) ==lim[1-x^2/2)]^(1/x^2) =lim[1-x^2/2)]^[(-2/x^2)*(-1/2)] =e^(-1/2)

柴昆侄4026在△ABC中,cos三次方x+cos(x+A)cos(x+B)cos(x+C)=0,求证tanx=cotA+cotB+cotC -
古茜春18495724521 ______[答案] 易知cosx及sinx都不为0,则已知式等价于 cos(x+A)/cosx*cos(x+B)/cosx*cos(x+C)/cosx+1=0 等价于 (cosA-tanxsinA)(cosB-tanxsinB)(cosC-tanxsinC)+1=0 等价于 (tanx-cotA)(tanx-cotB)(tanx-cotC)=1/(sinAsinBsinC) 下证1/(sinAsinBsinC)=(...

柴昆侄4026积分号cos的3次方乘以x乘以dx -
古茜春18495724521 ______[答案] ∫cos^3 x dx =∫cosxcos^2xdx =∫cosx(1-sin^2)dx =∫cosxdx-∫cosxsin^2xdx =-sinx-1/2∫sin2xsinxdx =-sinx-1/2∫(-1/2(cos(3x)-cosx)dx =-sinx+1/4∫cos3xdx-1/4∫cosxdx =-sinx+1/4*1/3∫cos3xd3x+1/4sinx =-3/4sinx-1/12sin3x+c

柴昆侄4026己知sin@ - cos@=1/2,求sin的3次方@ - cos的3次方的值. -
古茜春18495724521 ______[答案] sina-cosa=-1/2, 两边平方: 1-2sinacosa=1/4 sinacosa=3/8 (sina)^3-(cosa)^3 =(sina-cosa)(sin^2 a+sinacosa+cos^2 a) =(sina-cosa)(1+sinacosa) =(-1/2)(1+3/8) =-11/16