Definite Integral Challenge

Calculus Level 3

02(16x2)x16x2+(4x)(4+x)(12+x2)dx\large \int_{0}^{2}\frac{\left ( 16-x^2 \right )x}{16-x^2+\sqrt{\left ( 4-x \right )\left ( 4+x \right )\left ( 12+x^2 \right )}}\, dx

The integral above has a simple closed form. Find this closed form.

Give your answer to 3 decimal places.

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