# My fourth integration problem

Calculus Level 4

$\displaystyle \int_{0}^{{1} / {2} } \frac{dx}{\sqrt{9-36x^{2}-\arcsin^{2}(2x) +4x^{2} \arcsin^{2} (2x)}}$

If the integral above is equal to $$\displaystyle \dfrac{a}{b} \arcsin \left( \dfrac{\arcsin(c)}{d}\right)$$, where $$a,b,c$$ and $$d$$ are positive integers, with $$a, b$$ are coprime, find $$a+b+c+d$$.

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