Answer
$$ - 36$$
Work Step by Step
$$\eqalign{
& \int_0^{\ln 5} {{e^x}\left( {3 - 4{e^x}} \right)} dx \cr
& {\text{multiply}} \cr
& = \int_0^{\ln 5} {\left( {3{e^x} - 4{e^{2x}}} \right)} dx \cr
& {\text{integrating}} \cr
& = \left[ {3{e^x} - 2{e^{2x}}} \right]_0^{\ln 5} \cr
& {\text{evaluating the limits}} \cr
& = \left[ {3{e^{\ln 5}} - 2{e^{2\left( {\ln 5} \right)}}} \right] - \left[ {3{e^0} - 2{e^{2\left( 0 \right)}}} \right] \cr
& = \left[ {3\left( 5 \right) - 2\left( {25} \right)} \right] - \left[ {3\left( 1 \right) - 2\left( 1 \right)} \right] \cr
& = - 35 - 3 + 2 \cr
& = - 36 \cr} $$
