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F(x)=∫x2x3lnt dt\large F(x) = \int^{x^3}_{x^2} \ln t \ dt F(x)=∫x2x3lnt dt
F(x)F(x)F(x) is defined as above for x>0x>0x>0. If F′(2)=alnbF'(2) = a \ln bF′(2)=alnb, where aaa and bbb are positive integers with bbb being a prime, find a+ba+ba+b.
Note: F′(x)F'(x)F′(x) denotes the first derivative of F(x)F(x)F(x) with respect to xxx.
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