정적분 $\displaystyle \int _ {1} ^ {2} {x \arcsin \left (\frac{1} {x} \right) dx}$ 를 구하면?

• ①$\displaystyle \frac{\pi} {16} + \frac{\sqrt {3}} {2}$
• ②$\displaystyle \frac{\pi} {12} + \frac{\sqrt {3}} {2}$
• ③$\displaystyle \frac{\pi} {12} + \frac{\sqrt {3}} {3}$
• ④$\displaystyle \frac{\pi} {8} + \frac{\sqrt {3}} {3}$
• ⑤$\displaystyle \frac{\pi} {8} + \frac{\sqrt {3}} {2}$