Find the sum of the terms of the G.P., $\displaystyle a + ar + ar^2 + ...\ \infty$ where $\displaystyle a$ is the value of $\displaystyle x$ for which the function $\displaystyle 7 + 2x\log_{e}25 - 5^{x - 1} - 5^{2 - x}$ has the greatest value and $\displaystyle r$ is the limit $\displaystyle \lim_{x\rightarrow 0}\int_0^x \frac{t^2}{x^2\tan(\pi + x)} dt$