∫e的x次方乘以sin2xdx的不定积分是什么

Question

如题所述

Answer 1

∫e^xsin2xdx
=∫sin2xde^x
=e^xsin2x-∫e^xdsin2x
=e^xsin2x-2∫e^xcos2xdx
=e^xsin2x-2∫cos2xde^x
=e^xsin2x-2e^xcos2x+2∫e^xdcos2x
=e^xsin2x-2e^xcos2x-4∫e^xsin2xdx
所以∫e^xsin2xdx=(e^xsin2x-2e^xcos2x)/5+C