Question

Să se calculeze :

$\int \frac{3 {x}^{2} }{ \sqrt{ {x}^{3} + 1} } \: dx \: ,x > 0$

Answer 1

$\text{Facem schimbarea de variabila: }x^3+1=t\Rightarrow 3x^2dx=dt\\\text{Inlocuim:}\\\displaystyle\int \dfrac{3x^2}{\sqrt{x^3+1}} dx=\int \dfrac{1}{\sqrt t} dt= 2\sqrt t+C=2\sqrt{x^3+1}+C$