∫sin5xsin7xdx
谷河拜2655高数中的不定积分∫Sin3xSin5xdx=? -
徒闵肢18790248017 ______[答案] cos8x=cos(3x+5x)=cos3xcos5x-sin3xsin5xcos2x=cos(-2x)=cos(3x-5x)=cos3xcos5x+sin3xsin5x故sin3xsin5x=1/2*(cos2x-cos8x)∫Sin3xSin5xdx=∫1/2*(cos2x-cos8x)dx=1/4*sin2x-1/16*sin8x+C
谷河拜2655∫cos2x xdx -
徒闵肢18790248017 ______ ∫cos2x xdx =(1/2)∫cos2x xd2x =(1/2)∫xdsin2x =(1/2)xsin2x-(1/2)∫sin2xdx =(1/2)xsin2x-(1/4)∫sin2xd2x =(1/2)xsin2x+(1/4)cos2x+C
谷河拜2655∫sin3xsinxdx=? -
徒闵肢18790248017 ______ 预备知识 cos(A-B)=cosAcosB+sinAsinB cos(A+B)=cosAcosB-sinAsinB cos(A-B)-cos(A+B)=2sinAsinB ∴ sinAsinB=1/2[cos(A-B)-cos(A+B)] ∫sin3xsinxdx=1/2 ∫(cos2x-cos4x)dx=1/4 sin2x -1/8 sin8x +C
谷河拜2655∫sin(lnx)dx的不定积分 -
徒闵肢18790248017 ______[答案] ∫sin(lnx)dx=xsin(lnx)-∫xdsin(lnx)=xsin(lnx)-∫x*cos(lnx)*1/xdx=xsin(lnx)-∫cos(lnx)dx=xsin(lnx)-xcos(lnx)+∫xdcos(lnx)=xsin(lnx)-xcos(lnx)-∫x*sin(lnx)*1/xdx=xsin(lnx)-xcos(lnx)-∫sin(lnx)dx所以2∫s...
谷河拜2655高数 ∫2xcos2xdx -
徒闵肢18790248017 ______ ∫[0→π/2] 2xcos2x dx =∫[0→π/2] x d(sin2x) =xsin2x - ∫[0→π/2] sin2x dx =xsin2x + (1/2)cos2x |[0→π/2] =-(1/2) - (1/2) =-1 希望可以帮到你,不明白可以追问,如果解决了问题,请点下面的＂选为满意回答＂按钮,谢谢.
谷河拜2655∫(xcos2x)dx -
徒闵肢18790248017 ______ ∫(xcos2x)dx=(1/2)∫xdsin2x=(1/2)xsin2x-(1/2)∫sin2xdx=(1/2)xsin2x-(1/4)∫sin2xd2x=(1/2)xsin2x+(1/4)cos2x+C
谷河拜2655∫xsin2xdx= - ------ -
徒闵肢18790248017 ______ ∫(x²-1)sin2xdx=∫x²sin2xdx-∫sin2xdx=-1/2∫x²dcos2x+1/2cos2x=-1/2x²cos2x+1/2∫cos2xdx²+1/2cos2x=-1/2x²cos2x+∫xcos2xdx-1/2cos2x=-1/2x²cos2x+1/2∫xdsin2x-1/2cos2x=-1/2x²cos2x+1/2xsin2x-1/2∫sin2xdx-1/2cos2x=-1/2x²cos2x+1/2xsin2x+1/4cos2x-1/2cos2x+C
谷河拜2655请教如何解答?∫xcos(x/2)dx -
徒闵肢18790248017 ______ 用分部积分 ∫xcos(x/2)dx=2∫xcos(x/2)d(x/2)=2∫xdsin(x/2)=2xsin(x/2)-2∫sin(x/2)dx=2xsin(x/2)-4∫sin(x/2)d(x/2)=2xsin(x/2)+4cos(x/2)+C
谷河拜2655求不定积分 ∫ sin(ln x) dx -
徒闵肢18790248017 ______[答案] ∫sin(lnx)dx=xsin(lnx)-∫xdsin(lnx)=xsin(lnx)-∫xcos(lnx)*1/xdx=xsin(lnx)-∫cos(lnx)dx=xsin(lnx)-xcos(lnx)+∫xdcos(lnx)=xsin(lnx)-xcos(lnx)-∫sin(lnx)dx所以原式=(xsin(lnx)-xcos(lnx))/2+C
谷河拜2655∫2 sin 5x cos3x dx怎么会等于∫(sin8x+sin2x)dx 呢.谢谢…除了这个公式还有其他这样的公式吗? -
徒闵肢18790248017 ______[答案] 因为2sin5xcos3x=(sin5xcos3x+cos5xsin3x)+(sin5xcos3x-cos5xsin3x)=sin8x+sin2x 也可以用积化和差公式 sinxcosy=(1/2)*(sin(x+y)+sin(x-y))