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∫E^xsin^2xDx

∫ (e^x)sin²x dx = (1/2)∫ (e^x)(1 - cos2x) dx = (1/2)∫ e^x dx - (1/2)∫ (e^x)cos2x dx = (1/2)e^x - (1/2) • I I = ∫ (e^x)cos2x = (1/2)∫ e^x d(sin2x) = (1/2)(e^x)sin2x - (1/2)∫ (e^x)sin2x dx = (1/2)(e^x)sin2x - (1/2)(-1/...

【因为所用书写软件不能输入汉字,其中有个移项过程没有文字说明,请仔细查看。】 【第一行的第二个等号后面的第二项,移到第四行与其同类项合倂得5/2的系数。】

∫e^xsin2xdx =∫sin2xd(e^x) =e^xsin2x-∫e^xd(sin2x) =e^xsin2x-2∫e^xcos2xdx =e^xsin2x-2∫cos2xd(e^x) =e^xsin2x-2[e^xcos2x-∫e^xd(cos2x)] =e^xsin2x-2[e^xcos2x+2∫e^xsin2xdx] =e^xsin2x-2e^xcos2x-4∫e^xsin2xdx ∴5∫e^xsin2xdx=e^x(sin2x-2cos...

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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...

本题需要用倍角公式然后分开求积分,后面一部分用分部积分即可

答: 由cos2x=1-2(sinx)^2得:(sinx)^2=1/2-cos2x/2 ∫(sinx)^2dx =∫ 1/2-cos2x/2 dx =x/2-sin2x/4 + C

M=∫e^(-2x)sin(x/2)dx =(-1/2)∫sin(x/2)d[e^(-2x)] =(-1/2)sin(x/2)e^(-2x)-(-1/2)∫e^(-2x)d[sin(x/2)] =(-1/2)sin(x/2)e^(-2x)+(1/4)∫e^(-2x)cos(x/2)dx =(-1/2)sin(x/2)e^(-2x)+(-1/8)∫cos(x/2)d[e^(-2x)] =(-1/2)sin(x/2)e^(-2x)+(-1/8)cos(x...

e^x(sinx)^2=e^x[(1-cos2x)/2]=e^x/2-e^xcos2x/2。(e^xsin2x)'=2(cos2x)e^x+e^xsin2x(e^xcos2x)'=-2(sin2x)e^x+e^xcos2x。故可得:2(e^xsin2x)'+(e^xcos2x)'=5(cos2x)e^x。则e^xcos2x/2=[2(e^xsin2x)'+(e^xcos2x)']/10。故e^x(sinx)^2=e^x/2-[2(...

I = ∫e^x(sinx)^2dx = (1/2)∫e^x(1-cos2x)dx = (1/2)e^x - (1/2)∫e^xcos2xdx 其中 J = ∫e^xcos2xdx = ∫cos2xde^x = e^xcos2x + 2∫sin2xe^xdx = e^xcos2x + 2e^xsin2x - 2∫cos2xe^xdx = e^x(cos2x + 2sin2x) - 2J, 则 J = (1/3)e^x(cos2x + 2sin2...

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