------------------------------

                         Examples of procedure IntCS:



                 To test Theorem 1 of Seon-Hong Kim's article:

 On some integrals involving Chebyshev polynomials", Ramanujan J. v. 38 (201\
    5),

                                   (629-639)

           First part: i.e. Int(U_(2n)(x)*U*x_(2n)(x),x=-1..1).. Try:

                                                    2
             26  526   (4 n + 5) (4 n + 3)   2 (16 n  + 48 n + 39) N    2
     H1 := [[--, ---], ------------------- - ----------------------- + N ]
             15  315   (4 n + 9) (4 n + 7)     (4 n + 9) (4 n + 7)

                                      true



        Second part: i.e. Int(T_(2n)(x)*Star(T_(2n))(x),x=-1..1).. Try:

                                                        2
        -22  254     (4 n + 3) (2 n + 1) (4 n + 1) (20 n  + 61 n + 46)
H2 := [[---, ---], - --------------------------------------------------
        15   315                                          2
                     4 (4 n + 7) (2 n + 3) (4 n + 9) (20 n  + 21 n + 5)

              5         4         3          2
       (1920 n  + 4256 n  - 3496 n  - 13834 n  - 9621 n - 1890) N    2
     - ---------------------------------------------------------- + N ]
                                                2
           4 (4 n + 7) (2 n + 3) (4 n + 9) (20 n  + 21 n + 5)

                                      true



                   For Theorem 2 of that paper, First part:

                               [[-1/4], N + 1/4]

                                 Second part:

                               [[-1/8], N + 1/4]