Just for fun!

Calculus Level 4

Given that

{f(k,x)=(exlnk+eklnx+eklnk)dxf(e,0)=1f(4,3)=ab+cln2\begin{cases} f(k,x)=\displaystyle \int \left(e^{x \ln k}+e^{k \ln x}+e^{k \ln k}\right) dx \\ f(e,0)=1 \\ f(4,3)=\dfrac{a}{b}+\dfrac{c}{\ln 2} \end{cases}

Find a25bca-25 bc, where aa, bb and cc are positive integers with aa and bb being coprime integers.

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