We provide additional methods for the evaluation of the integral N-0,N-4(a; m) := integral(infinity)(0) dx/(x(4) + 2ax(2) + 1)(m+1), where m is an element of N and a is an element of (-1, infinity) in the form N-0,N-4(a; m) = pi/2(m+ 3/2)(a + 1)(m+1/2) Pm(a), where Pm(a) is a polynomial in a. The first one is based on a method of Schwinger to evaluate integrals appearing in Feynman diagrams, the second one is a byproduct of an expression for a rational integral in terms of Schur functions. Finally, the third proof is obtained from an integral representation involving modified Bessel functions.