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$\int \frac{d t}{\sqrt{2 a t - t^{2}}} = a^{x} \sin^{- 1} [\frac{t}{a} - 1]$ The value of x is

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Correct option is C

The quantity ta−1 is dimensionless i.e., [a]=[t]∴ 2at−t2=[t] or dt2at−t2=tt=M0L0T0 i.e. ax should also be dimensionless or x=0.

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∫dt2at−t2=axsin−1⁡ta−1 The value of x is

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$\int \frac{d t}{\sqrt{2 a t - t^{2}}} = a^{x} \sin^{- 1} [\frac{t}{a} - 1]$ The value of x is