Rational functions

 

In Derive

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

• integration

  w := int((3 a b^2-5 a^2 b)/(a^4-2),a)

                   2      2
              3 a b  - 5 a  b
      W :=   ----------------- da
                   4
                  a  - 2
  
  
                                                      2      
                           3/4             2       2 a  - 2            3/4
             3/4        a 2          3  2 b  LN  -----------      5 b 2    LN
        5 b 2    ATAN  --------                       2      
                          2                        2 a  + 2  
     - -------------------------- + -------------------------- + -------------
                   4                            8                            8
  
  
              1/4  
         a + 2     
        ---------- 
              1/4  
         a - 2     
       -------------

• verification by derivation

  dif(w,a);

       d     
       --  W 
       da    
  
  
                   2 a b (5 a - 3 b)
       - --------------------------------------
               2            1/4           3/4
          ( 2 a  + 2) (a + 2   ) ( 2 a - 2   )

  by using build the denominator is chosen

            2            1/4           3/4
       ( 2 a  + 2) (a + 2   ) ( 2 a - 2   )
  
  
          4
       2 a  - 4

  final result

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