Calculus #1

Calculus Level 3

F(x)=x2x3lnt dt\large F(x) = \int^{x^3}_{x^2} \ln t \ dt

F(x)F(x) is defined as above for x>0x>0. If F(2)=alnbF'(2) = a \ln b, where aa and bb are positive integers with bb being a prime, find a+ba+b.

Note: F(x)F'(x) denotes the first derivative of F(x)F(x) with respect to xx.

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