Word Count : 246

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We are asked to evaluate [ I = \int_0^5 \frac{dx}{\sqrt{5x - x^2}} ] using beta and gamma functions. First, rewrite the integrand in a suitable form. Factor the quadratic: [ 5x - x^2 = -x^2 + 5x = -(x^2 - 5x) = -\left(x^2 - 5x + \frac{25}{4} - \frac{25}{4}\right) ________ _________ ___ _____ ______.
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