# Just for fun!

Calculus Level 4

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

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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