Evaluate the following integrals: $(Simplify$ your answers$)$

$(a.),{\displaystyle \underset{-}{\overset{}{}}}{2}^{-3x}{e}^{x+6}{e}^{-2x}ln(e^{-2x})cos[\frac{x}{3}+\frac{}{6}]*(x+1)dx$

$(c.),{\displaystyle \underset{-}{\overset{}{}}}t{e}^{+-2}$ecos$[\frac{}{12}(larr5)]*(larr3)dt$

$(b.),{\displaystyle \underset{-}{\overset{+}{}}}x{e}^{x+3}{e}^{2x}cos[\frac{}{12}(x-6)]*(x-4)dx$

$(e.),{\displaystyle \underset{-}{\overset{}{}}}{x}^3{e}^{*1}{e}^{3}sin[\frac{}{12}(x-4)]*(x-2)dx$

$(d.),{\displaystyle \underset{-}{\overset{+}{}}}{x}^2{e}^{-2x}sin[x]*(x+A)dx$

$(f.),{\displaystyle \underset{-}{\overset{+}{}}}{x}^4{e}^{x+3}sin[\frac{}{6}(x-6)]*(x-2)dx$