Simple Definite Integral 2

Calculus Level 4

I=116ln(x)x(x+4)dx\large{ I = \int_1^{16} \dfrac{\ln(x)}{\sqrt{x}(x+4)} \, {d}x}

If II can be expressed as Aln(A)tan1(BC)A\ln(A) \tan^{-1} \left( \dfrac{B}{C} \right) where A,B,CA,B,C are positive integers with gcd(B,C)=1\gcd(B,C) = 1 and AA is a prime number. Then find the value of A+B+CA+B+C.

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