Question

Calcule a integral e marque a alternativa que corresponde ao resultado ∫ √ 4x +2 dx

Answer 1

$\displaystyle \sf \int \sqrt{4x+2} \ dx \\\\\\ \text{Fa{\c c}amos } : \\\\ u = 4x+2 \to du = 4dx \to dx = \frac{du}{u} \\\\ \text{Da{\'i}}: \\\\ \int \frac{\sqrt{u}\ du}{4} \\\\\\ \frac{1}{4}\int u^{\frac{1}{2}} \ du = \frac{1}{4} \cdot \frac{u^{\left(\frac{1}{2}+1\right)}}{\displaystyle \frac{1}{2}+1} + C \\\\\\ \frac{1}{4}\int u^{\frac{1}{2}} \ du = \frac{1}{4}\cdot \frac{u^{\frac{3}{2}}}{\displaystyle \frac{3}{2}} + C$

$\displaystyle \sf \int u^{\frac{1}{2}} \ du = \frac{1}{ 4}\cdot \frac{2\cdot \sqrt{u^3 }}{3} + C \\\\\\ \int u^{\frac{1}{2}} \ du = \frac{\sqrt{u^3}}{6}+C \\\\\\ \boxed{\ \sf \int \sqrt{4x+2} \ dx = \frac{\sqrt{(4x+2)^3}}{6} + C \ }$

Answer 2

Resposta:

R: 1/6 (4x+2) 3/2 +C