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You may not know integration , but using...

You may not know integration , but using dimensional analysis you can check on some results . In the integral `int ( dx)/(( 2ax - x^(2))^(1//2)) = a^(n) sin^(-1) ((x)/(a) -1)`, find the valiue of `n` .

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Let x = length. Therefore , `[ X] = [L]` and `[ dx] = [L]`.
By the principle of dimensional homogenity, `[(x)/(a)]` = dimensionless.
:. `[a] = [x] = [L]`
By substituting the dimension of each quantity in both sides,
`([L])/([L^(2) - L^(2)]^(1//2)) = [L^(n)] rArr n = 0`
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