Question

qual é a integral indefinida de ∫√3x+5 dx

Answer 1

Resposta:

$\displaystyle\int \sqrt{3x+5~} ~dx\\\\3x+5=u~\implies3dx=du~\implies dx=\frac{1 }{3} du\\\\\displaystyle\int \sqrt{3x+5}~dx=\displaystyle\int \sqrt{u}*\frac{1}{3}du =\frac{1}{3}\displaystyle\int u^{\frac{1}{2} }du =\frac{1}{3}*\frac{u^{\frac{1}{2}+1 } }{\frac{1}{2}+1 } +c=\frac{1}{3}*\frac{u^{\frac{3}{2} } }{\frac{3}{2} } +c=\frac{1}{3}*\frac{2}{3} u^{\frac{2}{3} }+c =\frac{2}{9} \sqrt{u^3} +c=\frac{2}{9} } \sqrt{(3x+5)^3} +c=\frac{2}{9} (3x+5)\sqrt{3x+5}$

Answer 2

Resposta:

2/9 (3x+5)^3/2 + c

Explicação passo a passo: