Answer
$$2\left( {3 + 5y} \right)$$
Work Step by Step
$$\eqalign{
& \int_4^9 {\frac{{3 + 5y}}{{\sqrt x }}} dx \cr
& {\text{the notation }}dx{\text{ indicates integration with respect to }}x,{\text{ so we treat }}x{\text{ as a variable and}} \cr
& y{\text{ as a constant}}{\text{. then}} \cr
& \int_4^9 {\frac{{3 + 5y}}{{\sqrt x }}} dx = \left( {3 + 5y} \right)\int_4^9 {\frac{1}{{\sqrt x }}} dx \cr
& = \left( {3 + 5y} \right)\int_4^9 {{x^{ - 1/2}}} dx \cr
& {\text{using the power rule }} \cr
& = \left( {3 + 5y} \right)\left( {\frac{{{x^{1/2}}}}{{1/2}}} \right)_4^9 \cr
& = 2\left( {3 + 5y} \right)\left( {\sqrt x } \right)_4^9 \cr
& {\text{evaluating the limits in the variable }}x \cr
& = 2\left( {3 + 5y} \right)\left( {\sqrt 9 - \sqrt 4 } \right) \cr
& {\text{simplifying}} \cr
& = 2\left( {3 + 5y} \right) \cr} $$
