Aloha :)
Willkommen in der Mathelounge...\o/
Eine Stammfunktion findest du hier mittels partieller Integration:
$$I=\int\underbrace{\frac14x}_{u}\cdot\underbrace{(16-x)^{1/2}}_{v'}\,dx=\underbrace{\frac14x}_{u}\cdot\underbrace{\left(-\frac23(16-x)^{3/2}\right)}_{v}-\int\underbrace{\frac14}_{u'}\cdot\underbrace{\left(-\frac23(16-x)^{3/2}\right)}_{v}\,dx$$$$\phantom{I}=-\frac x6(16-x)^{3/2}+\frac16\int(16-x)^{3/2}\,dx=-\frac x6(16-x)^{3/2}+\frac16\cdot\left(-\frac25(16-x)^{5/2}\right)+C$$$$\phantom I=-\frac{(16-x)^{3/2}}{30}\left(5x+2(16-x)\right)+C=-\frac{(16-x)^{3/2}}{30}\left(3x+32\right)+C$$
