Rational functions

 

In Reduce

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

• integration

  int((3*a*b^2-5*a^2*b)/(a^4-2),a);

                         1/4        a          1/4      1/4
      (sqrt(2)*b*( - 10*2   *atan(------) + 5*2   *log(2    + a)
                                    1/4
                                   2
  
                        1/4         1/4               1/4
                   - 5*2   *log( - 2    + a) + 3*log(2    + a)*b
  
                               1/4                           2
                   + 3*log( - 2    + a)*b - 3*log(sqrt(2) + a )*b))/8

• verification by differentiation

  df(ws,a);

       a*b*( - 5*a + 3*b)
      --------------------
              4
             a  - 2

• partial fraction decomposition

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

          5       2     3
      {-------,-------,---}
        x + 1   x - 2   x