Question

Calculati integrala:

Am nevoie de o indicatie.
Multumesc mult!!

Answer 1

Răspuns:

Explicație pas cu pas:

$u=x^{\frac{3}{2}}\Rightarrow du=\dfrac{3}{2}\sqrt{x}\\\displaystyle\int\dfrac{\sqrt{x}}{\sqrt{1-x^3}}dx=\dfrac{2}{3}\int\dfrac{1}{\sqrt{1-u^2}}du=\dfrac{2}{3}\arcsin u+C=\dfrac{2}{3}\arcsin x^{\frac{3}{2}}+C$