$\displaystyle \int _ {0} ^ {\infty} {\frac{1} {2x}} \left (\tan ^ {-1} \left (2023x \right) - \tan ^ {-1} \left (x \right) \right) dx$ 의 값은?

• ①$\displaystyle \frac{\pi} {8}$
• ②$\displaystyle \frac{\pi \ln \left (2023 \right)} {4}$
• ③$\displaystyle \frac{\pi \ln \left (2023 \right)} {2}$
• ④$\pi$