Evaluate the Integral by Making the Given Substitution $\int x^{2} \sqrt{x^{3}+2} d x, \quad \quad u=x^{3}+2$

Evaluate the integral by making the given substitution. $\int x^{2} \sqrt{x^{3}+2} d x, \quad \quad u=x^{3}+2$

A) $-\frac{2}{9}\left(x^{3}+2\right) ^{3 / 2}+C$
B) $\frac{2}{9}\left(x^{3}+2\right) ^{3 / 2}$
C) $\frac{1}{9}\left(x^{3}+2\right) ^{1 / 2}+C$
D) $\frac{2}{9}\left(x^{3}+2\right) ^{1 / 2}+C$
E) $\frac{2}{9}\left(x^{3}+2\right) ^{3 / 2}+C$

Correct Answer:

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