Question

e^xsin^2x原函数

e^xsin^2x原函数

Answer 1

∫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-2cos2x)
∴∫e^xsin2xdx=1/5*e^x(sin2x-2cos2x)+C

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