적분 $\displaystyle \int _ {1} ^ {2} {\frac{1+2x^2} {x \left (1+x^2 \right) ^2}} dx$ 의 값은?

• ①$\displaystyle \frac{3} {20} + \frac{1} {2} \ln \frac{3} {5}$
• ②$\displaystyle \frac{3} {20} + \frac{1} {2} \ln \frac{4} {5}$
• ③$\displaystyle \frac{3} {20} + \frac{1} {2} \ln \frac{6} {5}$
• ④$\displaystyle \frac{3} {20} + \frac{1} {2} \ln \frac{7} {5}$
• ⑤$\displaystyle \frac{3} {20} + \frac{1} {2} \ln \frac{8} {5}$