Question

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If $\int \frac{x^{\frac{1}{2}}}{\sqrt{a^3-x^3}} d x=P(x)+c$, then $\mathrm{P}(x)=$

MathematicsIndefinite IntegrationAP EAMCETAP EAMCET 2018 (24 Apr Shift 2)

Options:

A $\frac{1}{3} \operatorname{Sin}^{-1}\left(\frac{x^3}{a^3}\right)$
B $\frac{2}{3} \operatorname{Cos}^{-1}\left(\frac{x}{a}\right)$
C $\frac{2}{3} \operatorname{Sin}^{-1}\left(\frac{x}{a}\right)^{\frac{3}{2}}$
D $4^{\frac{1}{3}} \operatorname{Sin}^{-1}\left(\frac{x}{a}\right)^{\frac{1}{2}}$