Answer
$$14\left( {t\ln t - t} \right) + \frac{{{{9.6}^t}}}{{\ln 9.6}} + C$$
Work Step by Step
$$\eqalign{
& \int {\left( {14\ln t + {{9.6}^t}} \right)} dt \cr
& {\text{sum rule for derivatives}} \cr
& = \int {14\ln t} dt + \int {{{9.6}^t}} dt \cr
& {\text{use the constant multiple rule }}\int {kf\left( x \right)dx} = k\int {f\left( x \right)} dx \cr
& = 14\int {\ln t} dt + \int {{{9.6}^t}} dt \cr
& \cr
& {\text{Integrate using the rules of integration}} \cr
& \int {\ln x} dx = x\ln x - x + C,\,\,\,\,\int {{a^x}} dx = \left( {\frac{{{a^x}}}{{\ln a}}} \right) + C \cr
& \cr
& = 14\left( {t\ln t - t} \right) + \frac{{{{9.6}^t}}}{{\ln 9.6}} + C \cr} $$
