Integration(think differently)

Calculus Level 4

If I =\(\int \sqrt \frac{(5-x)}{(2+x)} .dx\) is of the form \(I=\sqrt (x+a) \sqrt (b-x)+c\sin^{-1} \sqrt \frac{x+d}{e} +k\) where k is constant of integration. Find \(a+b+c+d+e\)

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