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

• ①$\displaystyle x+ \frac{\sin 2x} {2} - \ln \left | x \right | + \ln \left | x-1 \right | +C$
• ②$\displaystyle -x + \frac{\cos 2x} {2} - \ln \left | x \right | + \ln \left | x-1 \right | +C$
• ③$\displaystyle x+ \frac{\cos x} {2} - \ln \left | x \right | + \ln \left | x-1 \right | +C$
• ④$\displaystyle x- \frac{\sin 2x} {2} - \ln \left | x \right | + \ln \left | x-1 \right | +C$
• ⑤$\displaystyle x- \frac{\cos x} {3} - \ln \left | x \right | + \ln \left | x-1 \right | +C$