Answer
$e^x+\dfrac{2}{3} x^{3/2}+C$
Work Step by Step
We are given that $I=\int (e^x+\sqrt x) \ dx$
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 $\int \int (e^x+\sqrt x) =e^x+ \dfrac{x^{3/2}}{3/2}+C$
or, $=e^x+ \dfrac{2x^{3/2}}{3}+C$
or, $=e^x+\dfrac{2}{3} x^{3/2}+C$
