# Bessel in AP?

Calculus Level 5

If

$\large \int x(2J_{2}(x)-4J_{4}(x)+6J_{6}(x)-\ldots) \ dx=\frac{x^{A}}{B}J_{k}(x)+c$

where $$A,B,k$$ are integers and $$c$$ is a constant of integration, find $$A^{B^{k}}$$.

$$J_{n}$$ are the Bessel functions of the first kind.

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