Integrate e^x sinx

Since we have two functions of x being multipied togrther, we have to integrate this by parts. Therefore if we say, u=sinx and v'=e^x, then u'=cosx and v=e^x.Applying the integration by parts rule of: uv' dx = vu - ∫vu' dxso: ∫e^xsinx dx = e^xsinx - ∫ e^xcosx dxAs before, since we have two functions of x being multipied togrther, we have to integrate this by parts. Therefore if we say, u=cosx and v'=e^x, then u'=-sinx and v=e^x.∫e^xsinx dx = e^xsinx - (e^xcosx - ∫ -e^xsinx dx)∫e^xsinx dx = e^xsinx - e^xcosx - ∫ e^xsinx dx2∫e^xsinx dx = e^xsinx - e^xcosx ∫e^xsinx dx = 1/2e^x(sinx-cosx)+c