\(f(k,x)=\displaystyle\int e^{x\ ln\ k}+e^{k\ ln\ x}+e^{k\ ln\ k} dx\)

Given that \(f(e,0)=1\), and \(f(4,3)=\dfrac{a}{b}+\dfrac{c}{ln\ 2}\)

Calculate \(a-25 bc.\)

**Details and assumptions**

\(a\) and \(b\) are co prime.

\(a,b,c\) are integers.

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