Integrate : $\int \sqrt {x^2+1} \log \large\frac{(x^2+1)-2 \log x }{x^4}$$dx$

Question

$(a)\;\frac{-1}{2}\bigg \{ \frac{2}{3} (1+\frac{1}{x^2})-(1+\frac{1}{x^2})^{3/2} \times \frac{4}{9}\bigg\}+c \\(b)\;\frac{1}{2}\bigg \{ \frac{2}{3} (1+\frac{1}{x^2})-(1+\frac{1}{x^2})^{3/2} \times \frac{4}{9}\bigg\}+c \\(c)\;\frac{-1}{2}\bigg \{ \frac{5}{3} (1+\frac{1}{x^2})-(1+\frac{1}{x^2})^{3/2} \times \frac{4}{9}\bigg\}+c \\ (d)\;None$