Answer
$\dfrac{117}{2}$
Work Step by Step
We are given that $I=\int_0^9 (x+\sqrt x) \ dx$
In order to solve the above integral, we will use the following formula such as:
$\int x^n \ dx=\dfrac{x^{n+1}}{n+1}+C$
Now, we have
$I=[\dfrac{x^2}{2}+\dfrac{x^{3/2}}{3/2}]_0^9$
or, $=[\dfrac{9^2}{2}+\dfrac{9^{3/2}}{3/2}]-[\dfrac{0}{2}+\dfrac{0^{3/2}}{3/2}]$
or, $=\dfrac{81}{2}+18$
or, $=\dfrac{117}{2}$
