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Questions  >>  EAMCET  >>  Mathematics
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Q)

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

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

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A)
$ (c)\;\frac{2}{3} \sin^{-1} \bigg( \sqrt {\frac{x^3}{a^3}}\bigg)$
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