All causes and sin are from the same root

Calculus Level 5

\[ \large \int_0^\infty \frac{ \sin(x) + \cos(x) }{\sqrt x} \, dx \]

If the integral above is equal to \( (A \times \pi)^B \) for rational numbers \(A \) and \(B\), find the value of \(A \div B \).

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