Evaluate: `int1/(x\ sqrt(a x-x^2))\ dx`

Explanation

Let,

`x=asin^2 theta`

`dx=2a sin theta cos theta d theta`

`=int1/(x\ sqrt(a x-x^2))\ dx`


`=int1/(asin^2 theta\ sqrt(a^2sin^2 theta -(asin^2 theta)^2))\ 2a sin theta cos theta d theta`


`=int(2a sin theta cos theta d theta)/(asin^2 theta\ asin theta cos theta)`


`=int(2 d theta)/(sin^2 theta\ a)`


`=int(2cosec^2 theta \ d theta)/(a)`


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