Question

Cálculo Diferencial e Integral II
Calcule :

∫√3x − 2 dx

Answer 1

Podemos aplicar o método da substituição, acompanhe:

$u=3x-2\\\\\frac{du}{dx}=3~~\rightarrow ~~dx=\frac{1}{3}du\\\\\\\int\sqrt{u}\,.\,\frac{1}{3}du\\\\\\\frac{1}{3}. \int u^{\frac{1}{2}}du\\\\\\\frac{1}{3}.\left(\frac{u^{\frac{1}{2}+1}}{\frac{1}{2}+1}\right)+C\\\\\\\frac{1}{3}.\left(\frac{u^{\frac{3}{2}}}{\frac{3}{2}}\right)+C\\\\\\\frac{2}{9}.\sqrt{u^3}+C\\\\\\Voltando~a~substituicao\\\\\boxed{\frac{2}{9}.\sqrt{(3x-2)^3}+C}$