Any integral of the form ∫ x^m J_n (x) dx can be evaluated in terms of Bessel functions and the indefinite integral ∫ J₀ (x) dx. The latter integral cannot be simplified further, but the function ∫^x₀ J₀ (t) dt is tabulated in Table 11.1 of Abramowitz and Stegun. Use the identities in Eqs. (22) and (23) to evaluate the integrals in Problems 11 through 18.

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dx [x² Jp(x)] = xP Jp-1(x). (22)