Answer
$$9{e^{0.2p}} + 6.2\sin p + C$$
Work Step by Step
$$\eqalign{
& \int {\left( {1.8{e^{0.2p}} + 6.2\cos p} \right)dp} \cr
& {\text{sum rule for derivatives}} \cr
& = \int {1.8{e^{0.2p}}} dp + \int {6.2\cos p} dp \cr
& {\text{use the constant multiple rule }}\int {kf\left( x \right)dx} = k\int {f\left( x \right)} dx \cr
& = 1.8\int {{e^{0.2p}}} dp + 6.2\int {\cos p} dp \cr
& \cr
& {\text{Integrate using the rules of integration}} \cr
& \int {\cos xdx} = \sin x + C,\,\,\,\,\int {{e^{ax}}} dx = \frac{1}{a}{e^{ax}} + C \cr
& \cr
& = 1.8\left( {\frac{1}{{0.2}}{e^{0.2p}}} \right) + 6.2\sin p + C \cr
& {\text{simplifying}} \cr
& = 9{e^{0.2p}} + 6.2\sin p + C \cr} $$
