# Integral of Bessel J for nu=2n

The following formula holds: $$\displaystyle\int_0^z J_{2n}(t)\mathrm{d}t=\displaystyle\int_0^z J_0(t) \mathrm{d}t -2\displaystyle\sum_{k=0}^{n-1} J_{2k+1}(z),$$ where $J_{2n}$ denotes the Bessel function of the first kind.