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∫1/(sin^2xCos^2x)

∫ 1/(sin²xcos²x) dx =∫ 4/(4sin²xcos²x) dx =4∫ 1/sin²2x dx =2∫ csc²2x d(2x) =-2cot2x + C 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。

∫1/sin²xcos²x dx =∫1/sin²x dx+∫1/cos²x dx =-cotx + tanx + c =tanx-cotx + c

∫sin^2x cos^2x dx =∫1/4*(sin2x)^2 dx =∫1/4*(1-cos4x)/2 dx =1/8*∫(1-cos4x)dx =1/8*(x-1/4*sin4x+C) =x/8-sin4x/32+C

=∫(cos^2x-sin^2x)/(cos^2xsin^2x)=∫(1/sin^2x - 1/cos^2x)=∫csc^2x-∫sec^2x=cotx-tanx

解:∫sin^3xcos^2xdx =-∫sin^2xcos^2xdcosx =-∫(1-cos^2x)*cos^2xdcosx =-∫(cos^2x-cos^4x)dcosx =(1/5)*cos^5x-(1/3)*cos^3x

后面sin那一项也是在分母上吗?

分母是立方和的立方? 不是立方和的平方?

cos2x=cos*2x-sin*2x cot*2x=csc*2x-1 cotx的导数=-csc*2x ∫(cos2x/sin^2x)dx=∫cos*2x-sin*2x/sin^2xdx 经过化简得 =∫cot*2xdx-∫1dx =∫csc*2xdx-∫1dx-∫1dx =-cotx-2x+c

sin²xcos²x =(1/4)(2sinxcosx)² =sin²(2x)/4 =[1-cos(2x)]/8 =1/8 -cos(2x)/8

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