Let the equation of a curve passing through the point \( (0,1) \) be given by \( y=\int x^{2} \c...

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Let the equation of a curve passing through the point \( (0,1) \) be given by \( y=\int x^{2} \cdot e^{x^{3}} d x \). If the equation of the curve is written in the form \( x=f(y) \) the \( f(y) \) is
(a) \( \sqrt{\log _{e}(3 y-2)} \)
(b) \( \sqrt[3]{\log _{e}(3 y-2)} \)
(c) \( \sqrt[3]{\log _{e}(2-3 y)} \)
(d) none of these
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