All causes and sin are from the same root

Calculus Level 5

0sin(x)+cos(x)xdx \large \int_0^\infty \frac{ \sin(x) + \cos(x) }{\sqrt x} \, dx

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

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