The value of ( n ) is
(a) 0
(b) -1
( (c) 1 )
(d) none of these

( int frac{d x}{sqrt{2 a x-x^{2}}}=int frac{d x}{sqrt{a^{2}-left(x^{2}-2 a x+a^{2}right)}} )
( =int frac{d x}{sqrt{a^{2}-(x-a)^{2}}} sin ^{-1}left(frac{x-a}{a}right)=sin ^{-1}left(frac{x}{a}-1right) )
( =sin ^{-1}left(frac{x}{a}-1right)=a^{n} sin ^{-1}left(frac{x}{a}-1right) )
( Rightarrow {a^{n}=1})  ({n=0} ) Option (a)