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∫xCos^3 xDx

∫xcos^3 xdx =∫xcos^2 xcosxdx =∫xcos^2 xdsinx =∫x(1-sin^2 x)dsinx =∫xdsinx-∫xsin^2 x dsinx =xsinx-∫sinxdx-1/3∫xdsin^3 x =xsinx+∫dcosx-1/3(xsin^3 x -∫sin^3 x dx) =xsinx+cosx-xsin^3 x/3+1/3∫sin^2xsinxdx =xsinx+cosx-xsin^3 x/3-1/3∫...

=(1/3)x²sin3x+(2/9)xcos3x-(2/27)sin3x + c

(3sin3x+cos3x)*e^x/10+C.

这个我不知道发图片!我说下思路吧!先把分母sinx变成2sinx/2cosx/2 然后三次方后就可以和分子约去cosx/2的三次方!!简化后的式子直接分部积分(cosx/2/sinx/2^3这个整体是一个函数的导数),只要一步就能出来答案!!

如图

x^2*sin3xdx = -1/3∫x^2dcos3x = -1/3x^2cos3x+2/3∫xcos3xdx = -1/3x^2cos3x+2/9∫xdsin3x = -1/3x^2cos3x+2/9xsin3x-2/9∫sin3xdx = -1/3x^2cos3x+2/9xsin3x+2/27cos3x+C

定积分偶倍奇零 =2∫(0.π/2)sin²xcos²xdx =1/2∫sin²2xdx =1/4∫1-cos4xdx =x/4-sin4x/16 =π/8

记A=∫e^2xsin3xdx 用分部积分法: A=0.5e^(2x)sin3x-∫0.5e^(2x)3cos3xdx =0.5e^(2x)sin3x-1.5∫e^(2x)cos3xdx =0.5e^(2x)sin3x-1.5[0.5e^(2x)cos3x+∫0.5e^(2x)3sin3xdx] =0.5e^(2x)sin3x-0.75e^(2x)cos3x-2.25∫e^(2x)sin3xdx =0.5e^(2x)sin3x-0.7...

d(cosx^3)=3*cosx^2*-sinx*dx,不等于sinx^2

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