Question

Wie lautet die Stammfunktion zu f(x)=0,25*wurzel(x+4) ?

Answer 1

Substitution \(u=x+4, \frac{du}{dx}=1, dx=du\)

$$\int 0,25\sqrt{x+4} \, dx=0,25\int \sqrt{u} \, du=0,25\int u^{\frac{1}{2}} \, du=0,25\cdot \frac{2}{3}u^\frac{3}{2}$$ $$=\frac{1}{6}(x+4)^\frac{3}{2}=\frac{1}{6}\sqrt{(x+4)^3}$$