The integral $\;\int_{0}^{\large\frac{1}{2}} \large\frac{ln(1+2x)}{1+4x^{2}} dx\;$ , equals :

Question

$(a)\;\large\frac{\pi}{4}\; \normalsize ln2\qquad(b)\;\large\frac{\pi}{8}\; \normalsize ln2\qquad(c)\;\large\frac{\pi}{16}\; \normalsize ln2\qquad(d)\;\large\frac{\pi}{32}\; \normalsize ln2$