A Definite Problem

Calculus Level 4

\[ \large \int_{\sqrt{\ln 2}}^{\sqrt{ \ln 3}} \dfrac {x \sin (x^2)}{\sin(x^2) + \sin(\ln 6 - x^2)} \, dx \]

The integral above has a closed form. Find the value of this closed form.

Give your answer to 3 decimal places.

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