Calculus with Absolute Values

Calculus Level 3

\[f(x)=\dfrac{x}{\left | x^{3} \right |} ,\quad g(x)=f'(x)+1\]

The lines of the tangents of \(f(x)\) and \(g(x)\) at their negative intersecting point form a triangle of area \(A\) with the \(y\)-axis. Find the value of integer \(A\).

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