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If equation $\int \frac{dt}{\sqrt{3 at - 2 t^{2}}} = a^{x} \sin^{- 1} (\frac{t^{2}}{a^{2}} - 1)$ , the value of x is

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(t2a2-1) is dimensionless∴[a] = [t]As, (3at-2t2) = [t]∴ [dt3at-t2]= [t][t]= [M0L0T0]ax should be dimensionless, so x = 0.

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If equation ∫dt3at-2t2 = axsin-1(t2a2-1), the value of x is

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If equation $\int \frac{dt}{\sqrt{3 at - 2 t^{2}}} = a^{x} \sin^{- 1} (\frac{t^{2}}{a^{2}} - 1)$ , the value of x is