Calcolare i seguenti integrali:

a) $\displaystyle \int \frac{x^2+2}{x^2} \, \mathrm {d} x=\int 1 \, \mathrm {d} x+\int \frac{2}{x^2} \, \mathrm {d} x=x-\frac{2}{x}+c$

b) $\displaystyle \int \frac{\sqrt{x}+x}{\sqrt{x}} \, \mathrm {d} x=\int 1 \, \mathrm {d} x+\int x^{\frac{1}{2}} \, \mathrm {d} x=$

$\displaystyle =x+\frac{1}{\frac{3}{2}}x^{\frac{3}{2}}+c=x+\frac{2}{3}x^\frac{3}{2}+c=x+\frac{2}{3}\sqrt{x^3}+c$