【正确答案】∫e^xsin²xdx=
而∫e^xcos 2xdx=∫cos2xde^x
=e^xcos 2x+2∫sin 2x.e^xdx
=e^xcos 2x+2∫sin 2xde^x=e^xcos 2x+2e^xsin 2x一4∫e^xcos 2xdx，