Question

Calcule a integral e marque a alternativa que corresponde ao resultado.

∫√4x+2 dx

Answer 1

Resposta:

$\frac{1}{6} (4x+2)+c$

Explicação passo a passo:

$\displaystyle\int \sqrt{4x+2}dx\\\\4x+2=u \implies4dx=du \implies dx=\frac{1}{4} du\\\\ \displaystyle\int \sqrt{4x+2} =\displaystyle\int \sqrt{u}*\frac{1}{4} du=\frac{1}{4} \displaystyle\int \sqrt{u}du=\frac{1}{4} \displaystyle\int u^{\frac{1}{2} }du=\frac{1}{4}} *\frac{u^{\frac{3}{2} } }{\frac{3}{2} }+c=\\\\\frac{1}{4}*\frac{2}{3}u^{\frac{3}{2} }+c=\frac{1}{6}(4x+2)^{\frac{3}{2} }+c$

Answer 2

Resposta:

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