The value of $$\int_{\sqrt{\ln 2}}^{\sqrt{\ln 3}} \frac{x \sin x^2}{\sin x^2 + \sin(\ln 6 - x^2)} dx $$ is

A

$$\frac{1}{4} \ln \frac{3}{2}$$

B

$$\frac{1}{2} \ln \frac{3}{2}$$

C

$$\ln \frac{3}{2}$$

D

$$\frac{1}{6} \ln \frac{3}{2}$$