log

(%i1)f1(xi):= 1-xi^2;
                                               2
(%o1)                          f1(xi) := 1 - xi
(%i2) f2(xi):= log(1/xi);
                                             1
(%o2)                          f2(xi) := log(--)
                                             xi
(%i3) integrate(xi*f1(xi),xi,k,1);
                                  4      2
                                 k  - 2 k  + 1
(%o3)                            -------------
                                       4
(%i4) integrate(xi*f2(xi),xi);
                                 2     2
                               xi    xi  log(xi)
(%o4)                          --- - -----------
                                4         2
(%i5)

Run Example

e1: 2*(2*a*log(y)+a*log(x));
(%o1)                      2 (2 a log(y) + a log(x))
(%i2) logcontract(e1);
                                        2  4
(%o2)                            a log(x  y )
(%i3) e2:-4*log(4)/3  + log(3)+ 2 *log(2) + 1;
                        4 log(4)
(%o3)                 - -------- + log(3) + 2 log(2) + 1
                           3
(%i4)  logcontract(e2);
                                      4 log(4)
(%o4)                       log(12) - -------- + 1
                                         3
(%i5)

Run Example

diff(log(%e));
(%o1)                                  0
(%i2)

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