Unfamiliar integral.

If the integral $\Phi(n,k,m,r,p)=\int_0^1\left(\frac{\ln x^{-n!}\cdot \ln x^{-k!}}{\ln x^{-m^2} \cdot \ln x^{-r^2}\cdot \ln x^{-p!}}\right)^{dx}$ and $\sum_{m=1}^{\infty}\sum_{r=1}^{m}\Phi\left(\frac{1}{2},\frac{3}{2},m,r,\frac{3}{4}\right)=\frac{\Gamma\left(\frac{1}{b}\right) e^{\gamma}}{\sqrt{a}}\cdot \frac{c\pi^{b}}{d}$ where $a,b,c$ and $d$ are positive integers with $\text{g.c.d}(c,d)=1$ . Find the value of $a+b+c+d$ .

This is an original and proposed problem to prove the closed form .