Too many variables

$f\left(a,b,c\right) = \displaystyle\int_{0}^{a}{(a^b-x^b)^c\,dx}$

$f\left(a,b,c\right) = a^b\displaystyle\int_{0}^{a}{(a^b-x^b)^{c-1}\,dx} - \displaystyle\int_{0}^{a}{(x)(x^{b-1})(a^b-x^b)^{c-1}\,dx}$

$f\left(a,b,c\right) = a^bf\left(a,b,c-1\right) - \displaystyle\int_{0}^{a}{(x)(x^{b-1})(a^b-x^b)^{c-1}\,dx}$

Consider the integral $I =\displaystyle\int_{0}^{a}{(x)(x^{b-1})(a^b-x^b)^{c-1}\,dx}$

Using integration by parts $I = \bigg(- \displaystyle\frac{x(a^b-x^b)^c}{bc}\bigg)\Bigg|_0^a + \displaystyle\frac{1}{bc}\displaystyle\int_{0}^{a}{(a^b-x^b)^c\,dx}$

$I = 0 + \displaystyle\frac{1}{bc}f\left(a,b,c\right)$

Resubstituting the value of $I$ we get

$f\left(a,b,c\right) = a^bf\left(a,b,c-1\right) - \displaystyle\frac{1}{bc}f\left(a,b,c\right)$

Thus $\displaystyle\frac{f\left(a,b,c\right)}{f\left(a,b,c-1\right)} = \displaystyle\frac{a^bbc}{bc+1}$

Thus $g\left(a,b,c\right) = \displaystyle\frac{a^bbc}{bc+1}$

Therefore $g\left(5,6,104\right) = \displaystyle\frac{5^6(6)(104)}{(6)(104)+1} = 15600$

$100K = 15600$

$K=156$