Rational functions

 

In Macsyma

For comparison with other CAS choose from: Axiom Derive Maple Mathematica Reduce

rf: (3*a*b^2-5*a^2*b)/(a^4-2);

                                 2      2
                            3 a b  - 5 a  b
                           ---------------
                                4
                               a  - 2

• integration

  integrate(rf, a);

                                                                     1/4
                                                                a - 2
                                                          5 log(--------)
                 2                       2                           1/4
          3 log(a  + sqrt(2)) b   3 log(a  - sqrt(2)) b         a + 2
     - b (--------------------- - --------------------- + ---------------
                4 sqrt(2)               4 sqrt(2)                1/4
                                                              4 2
                                                                        a
                                                                5 atan(----)
                                                                        1/4
                                                                       2
                                                              + ------------)
                                                                      1/4
                                                                   2 2

• partial fraction decomposition

  partfrac((10*x^2-11*x-6)/(x^3-x^2-2*x), x);

                              5     3     2
                            ----- + - + -----
                            x + 1   x   x - 2