= Solution
In the central <classically forbidden region>, define the positive decay <momentum> $\chi(x)=\sqrt{2m[V(x)-E]}$ and the <dimensionless> <action integral> $K(x)=\hbar^{-1}\int_x^{x_1}\chi(y)\,dy$. The general leading <WKB approximation> is
$$
\boxed{\psi_{\rm I}(x)\simeq\frac{A e^{K(x)}+B e^{-K(x)}}{\sqrt{\chi(x)}},\qquad 0<x<x_1.}
$$
Both coefficients are allowed: this interval has finite length, so the exponential that grows towards the barrier centre cannot be discarded by a condition at infinity. The <WKB validity condition> holds away from the <classical turning point> $x_1$; a local <Airy function> solution supplies its continuation there.
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