Non-elementry closed form

If the integral $\int_0^{\frac{1}{2}}\dfrac{\tanh^{-1} x}{\sqrt[5]{x}}dx =\dfrac{5}{\sqrt[a]{b^c}}\left(\ln d-\dfrac{c}{e} {}_2F_1\left(\frac{p}{q},1,\frac{r}{q},\frac{1}{s}\right)\right)$ where all the unknowns are positive integers with $a,b,d$ are primes, then find the sum of all positive integers.

The original problem belongs to Sir Srinivasa Raghava where he proposed to evaluate the integral in closed form, ie; $\int_0^{\frac{1}{2}}\frac{\tanh^{-1}x}{\sqrt[5]{x}} dx$

Notation: ${}_2F_1(a,b;c;z)$ is Gaussian hypergeometric function.