∫e^x(sinx)^2dx

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∫e^x(sinx)^2dx
∫e^x(sinx)^2dx

∫e^x(sinx)^2dx
∫e^x(sinx)^2dx
=1/2∫e^x(1-cos2x)dx
=1/2∫(e^x-e^xcos2x)dx
=1/2∫e^xdx-1/2∫e^xcos2xdx
=1/2e^x-1/2∫e^xcos2xdx
∫e^xcos2xdx
=∫cos2xde^x
=e^xcos2x+2∫e^xsin2xdx
=e^xcos2x+2∫sin2xde^x
=e^xcos2x+2e^xsin2x-4∫e^xcos2xdx
5∫e^xcos2xdx=e^xcos2x+2e^xsin2x=e^x(cos2x+2sin2x)
∫e^xcos2xdx=1/5e^x(cos2x+2sin2x)
所以,原式1/2e^x-1/10e^x(cos2x+2sin2x)+C

∫e^x(sinx)^2dx
=∫(sinx)^2d(e^x)
=e^x(sinx)^2-2∫e^xsinxcosxdx
=e^x(sinx)^2-∫e^xsin2xdx
又
∫e^xsin2xdx
=∫sin2xd(e^x)
=e^xsin2x-2∫e^xcos2xdx
=e^xsin2x-2∫cos2xd(e^x)
=e^...

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∫e^x(sinx)^2dx
=∫(sinx)^2d(e^x)
=e^x(sinx)^2-2∫e^xsinxcosxdx
=e^x(sinx)^2-∫e^xsin2xdx
又
∫e^xsin2xdx
=∫sin2xd(e^x)
=e^xsin2x-2∫e^xcos2xdx
=e^xsin2x-2∫cos2xd(e^x)
=e^xsin2x-2e^xcos2x-4∫e^xsin2xdx
所以 5∫e^xsin2xdx=e^xsin2x-2e^xcos2x
∫e^xsin2xdx=(e^xsin2x-2e^xcos2x)/5
所以
原定积分=e^x(sinx)^2-(e^xsin2x-2e^xcos2x)/5+C

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∫(x/2+e^x+sinx)dx ∫ e^2x sinx dx .. ∫e^x(sinx)^2dx ∫[e^sin2x*(sinx)^2]/e^2x dx ∫(x sinx)e^x dx ∫[e^(－2x)sinx/2]dx ∫e^(-2x)*(cosx-sinx)dx=? 求不定积分：∫e^x(sinx)^2dx ∫e^x(sinx)^2dx怎么求如图不定积分：e^x(sinx)^2dx 求不定积分：1.∫e^(sinx)[x(cosx)^3-sinx]/(cosx)^2dx 2.∫[e^(3x)+e^x]/[e^(4x)-e^(2x)+1]dx d/dx积分号e^-x^2 sinx dx= ∫(sinx-x^2)dx ∫x/(sinx)^2dx ∫ x/(sinx)^2dx 1.∫(sinx)^5(cosx)^3dx 2.∫(sinx)²(cosx)²dx 3.∫（e^x²+2x²e^x²）dx ∫(e^x+sinx)/(e^x-cosx)dx ∫（e^sinx）*x*(cosx)^3-sinx/(cosx)^2 dx