∫eˣ cosxdx求值为多少？

Question

如题所述

Answer 1

∫e^x.cosx dx
=∫cosx de^x
=e^x.cosx +∫e^x.sinx dx
=e^x.cosx +∫sinx de^x
=e^x.cosx +e^x.sinx -∫e^x.cosx dx
2∫e^x.cosx dx =e^x.cosx +e^x.sinx
∫e^x.cosx dx =(1/2)[e^x.cosx +e^x.sinx] + C

Answer 2

∫eˣcosxdx
=∫eˣd(sinx)
=eˣsinx-∫sinxd(eˣ)
=eˣsinx+∫eˣd(cosx)
=eˣsinx+eˣcosx+C -∫eˣcosxdx
2∫eˣcosxdx=eˣsinx+eˣcosx +C
∫eˣcosxdx=½(sinx+cosx)eˣ+C