If $\int \sqrt {\large\frac{x}{a^3-x^3}}dx=g(x)+c,$ then $g(x)$ is equal to :

Question

$$\begin {array} {1 1} (a)\;\frac{2}{3} \cos^{-1} x & \quad (b)\;\frac{2}{3} \sin^{-1} \bigg(\frac{x^3}{a^3}\bigg) \\ (c)\;\frac{2}{3} \sin^{-1} \bigg( \sqrt {\frac{x^3}{a^3}}\bigg) & \quad (d)\;\frac{2}{3} \cos^{-1} \bigg(\frac{x}{a} \bigg) \end {array}$$