  In the world of mathematical analysis, many counterintuitive answers arise
from the manipulation of seemingly unrelated concepts, ideas, or functions. For
example, Euler showed that $e^{i\pi} + 1 = 0$, whereas Gauss proved that the
area underneath $y = e^{-x^2}$ spanning the whole real axis is $ \sqrt{\pi} $.
In this paper, we will determine the closed-form solution of the improper
integral \[ I_n = \int_{0}^{\infty} \frac{\ln{x}}{x^n+1} dx, \ \forall n \in
\mathbb{R} \text{, with}\ n > 1. \] Determining closed-form solutions of
improper integrals have real implications not only in easing the solving of
similar, yet more difficult integrals, but also in speeding up numerical
approximations of the answer by making them more efficient. Following our
calculations, we derived the formula \[ I_n = \int_{0}^{\infty}
\frac{\ln{x}}{x^n+1} dx =
-\frac{\pi^2}{n^2}\cot{\frac{\pi}{n}}\csc{\frac{\pi}{n}} = -\frac{d}{dn} \Bigg[
\Gamma\Big(1-\frac{1}{n}\Big) \Gamma\Big(\frac{1}{n}\Big) \Bigg]. \]

General Mathematics