Limit of a Definite Integral #5

Calculus Level 4

L=limnnndx(x2+1)(ex+1)\large{L=\lim_{n \to \infty} \int_{-n}^{n} \dfrac{dx}{(x^2+1)(e^x+1)}}

If LL can be expressed as πAB{\dfrac{\pi^A}{B}} where A,BA,B are positive integers, then find the value of A+BA+B.

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