# It only looks scary

Calculus Level 4

$\large \large \lim_{x\to0}\dfrac{\ln(1+\sin^3x \cos^2x)\cot(\ln^3(1+x))\tan^4x}{\sin(\sqrt{x^2+2}-\sqrt{2})\ln(1+x^2)}$

If the limit above is equal to $$a\sqrt b$$, where $$a$$ and $$b$$ are integers with $$b$$ square-free, find $$a+b$$.

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