Question

como resolvo essa integral. S z² vezes raiz quadrada 3z

Answer 1

$\displaystyle\int{z^{2}\cdot \sqrt{3z}\;dz}\\ \\ \\ =\int{z^{2}\cdot \sqrt{3}\cdot \sqrt{z}\;dz}\\ \\ \\ =\sqrt{3}\int{z^{2}\cdot \sqrt{z}\;dz}\\ \\ \\ =\sqrt{3}\int{z^{2}\cdot z^{1/2}\;dz}\\ \\ \\ =\sqrt{3}\int{z^{2+(1/2)}\;dz}\\ \\ \\ =\sqrt{3}\int{z^{5/2}\;dz}\\ \\ \\ =\sqrt{3}\cdot \dfrac{z^{(5/2)+1}}{\frac{5}{2}+1}+C$

$=\sqrt{3}\cdot \dfrac{z^{7/2}}{\frac{7}{2}}+C\\ \\ \\ =\dfrac{2\sqrt{3}}{7}\,z^{7/2}+C$