Answer
$\displaystyle\int$$\frac{x^{2}}{\sqrt{(x^{3}+3)}}$ dx = $\frac{2}{3}\sqrt{(x^{3}+3)}$ +c where c is an arbitrary constant
Work Step by Step
To solve this integral, we will attempt to find the derivative and antiderivative pair.
$\frac{d}{dx}\sqrt(x^{3}+3)$ = $\frac{1}{2}(x^{3}+3)^{-\frac{1}{2}}(3x^{2})$
=$\displaystyle\int$$\frac{3x^{2}}{2\sqrt(x^{3}+3)}$ dx
$\displaystyle\int$$\frac{x^{2}}{\sqrt(x^{3}+3)}$ dx = $\frac{2}{3}\displaystyle\int$$\frac{3x^{2}}{2\sqrt(x^{3}+3)}$ dx
=$\frac{2}{3}\sqrt{(x^{3}+3)}$ +c where c is an arbitrary constant
