Answer
$\int(t^{\frac{1}{2}}+1) (t+1) dt= \frac{2}{5}t^{\frac{5}{2}}+ \frac{2}{3}t^{\frac{3}{2}}+ \frac{1}{2}t^2 +C $
Work Step by Step
$\int(t^{\frac{1}{2}}+1) (t+1) dt= \int(t^{\frac{3}{2}}+t^{\frac{1}{2}}+t+1) dt= \frac{1}{\frac{5}{2}}t^\frac{5}{2} + \frac{1}{\frac{3}{2}} t^{\frac{3}{2}}+\frac{1}{2}t^2 +t +C= \frac{2}{5}t^{\frac{5}{2}}+ \frac{2}{3}t^{\frac{3}{2}}+ \frac{1}{2}t^2 +C $
