Constant Integrand?

Calculus Level 4

\[\large \int_{-1}^3 \left(\arctan\left(\dfrac x{1+x^2}\right) + \arctan\left(\dfrac {1+x^2}x \right)\right) \, dx\]

If the above integral can be expressed as \(A\pi^B\), where \(A\) and \(B\) are natural numbers. Find \(A+B\)

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