Integrate: $\int \large\frac{1}{x \sqrt {x\log (x^2) -5}}$$dx$

Question

$(a)\;\log | \log x^2 +\sqrt {\log x^2 -\sqrt 5}|+c\\(b)\; \log | \log x^2 +\sqrt {\log x^2 + \sqrt 5}|+c\\(c)\; 2\log | \log x^2 +\sqrt {\log x^2-\sqrt 5}|+c \\ (d)\;None$