Constant Integrand?

Calculus Level 3

13(arctan(x1+x2)+arctan(1+x2x))dx\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 AπBA\pi^B, where AA and BB are natural numbers. Find A+BA+B

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