In the equation ` int (dx)/sqrt(2ax - x^(2) ) = a^(2) sin ^(-1) [(x)/(a) - 1]`. Find the value of n .

int(dx)/(sqrt(2)ax-x^(2))=a^(n)sin^(-1){(x-a)/(a)}a->

If 2y=(x-a)sqrt(2ax-x^(2))+a^(2)"sin"^(-1)(x-a)/(a) , then the value of (dy)/(dx) is equal to -

int(2sin^-1x)/sqrt(1-x^2)dx =

int(dx)/(sqrt(1-x^(2))(sin^(-1)x)^(2))

Given that int (dx)/(sqrt(2 ax - x^2)) = a^n sin^(-1) ((x-a)/(a)) where a is a constant. Using dimensional analysis. The value of n is