First, let's write 6.4 as a fraction to make it a bit easier to work with. [tex]\int\ {\frac{32}{5}e^{-3x+6}} \, dx[/tex] [tex]=\frac{32}{5} \int\ {e^{-3x+6}} \, dx[/tex] Use u-substitution: [tex]u=-3x+6[/tex] [tex]du=-3dx[/tex] So we now have [tex]\frac{32}{5}*-\frac{1}{3} \int {-3e^{-3x+6}} \, dx[/tex] [tex]=-\frac{32}{15} \int {e^{u}} \, du[/tex] [tex]=-\frac{32}{15}e^{u}+C[/tex] [tex]=-\frac{32}{15}e^{-3x+6}+C[/tex]
(If you want the answer to have a decimal, then [tex]-\frac{32}{15}[/tex] is -2.133333...)
