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sinxsin2x

因为cosX- cos3X =cos(2x-x)-cos(2x+x) =cos2xcosx+sin2xsinx -(cos2xcosx-sin2xsinx) =2sin2xsinx

∫sinxsin2xdx =-1/2∫(cos3x-cosx)dx =-1/2[1/3sin3x-sinx]+C =-1/6sin3x+1/2sinx+C

∫(sinxsin2x)dx =2∫sin²xcosxdx =2∫sin²xdsinx =2sin³x/3+C

y=sinxsin2x y^2=sin^2x*4*sin^2x*cos^2x=2sin^2x*sin^2x*(2cos^2x)

其实一般都是2π,特殊抵消的才会是其他

利用积化和差公式-2sin((A+B)/2)*sin((A-B)/2)=cosA-cosB 2sin(x/2)*sinx=cos(x/2)-cos(3x/2) 2sin(x/2)*sin2x=cos(3x/2)-cos(5x/2) ... 2sin(x/2)*sinnx=cos((2n-1)x/2)-cos((2n+1)x/2) 裂项相消 原式就等于cos(x/2)-cos((2n+1)x/2)

积化和差∫sinxsin2xsin3xdx=1/2∫(cosx-cos3x)sin3xdx=1/2∫cosxsin3xdx-1/2∫cos3xsin3xdx=1/4∫(sin2x+sin4x)dx-1/4∫sin6xdx=-1/8cos2x-1/16cos4x+1/24cos6x+C数学软件验算:

∫(e^sinx)*sin2x dx (由倍角公式:sin2x=2sinxcosx) =2∫(e^sinx)*sinxcosx dx (cosxdx=d(sinx)) =2∫(e^sinx)*sinx d(sinx) (令sinx=y) =2∫y*e^y dy =2∫y d(e^y) =2(ye^y-∫e^y dy) =2(ye^y-e^y+C) (将 y=sinx 代回) =2(sinx*e^sinx-e^sinx)+C 其...

sin2x=2sinxcosx X的正弦平方+X的余弦平方=1 两个式子两个未知数不就解出来了么

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