[tex]\displaystyle \sf \int \sqrt{ax+b}\ dx \\\\ \text{Fa{\c c}amos }: \\\\ ax+b= u \to a\cdot dx = du \to dx = \frac{du }{a}\\\\ Da{\'i}} : \\\\ \int \sqrt{u}\ \frac{du }{a} \\\\\\ \frac{1}{a}\cdot \int u^{\frac{1}{2}} \ du \\\\\\ \frac{1}{a} \cdot \frac{u^{\left(\frac{1}{2}+1\right)}}{\displaystyle \sf \frac{1}{2}+1} + C\\\\\\ \frac{1}{a}\cdot \frac{u^{\frac{3}{2}}}{\displaystyle \frac{3}{2}} + C \\\\\\ Portanto :[/tex]

[tex]\displaystyle \boxed{\sf \ \int \sqrt{ax+b}\ dx = \frac{2\cdot \sqrt{\left( ax+b\right )^{3}}}{3\cdot a} + C \ }\checkmark[/tex]