is it possible to add an integration rule to Maple int?

Question

I'd like Maple to return ln(abs(x)) for int(1/x,x) instead of ln(x).

Is there a way to give a rule using a pattern, for int to use in this case as it is possible to do in Mathematica? i.e. somehow to override int result for a specific result like the above? Or may be there is some global option one can set?

Maple 2018.1

Answer 1

A procedure way:

 REALINT2 := proc (f, x) local func, a; 
 func := int(f, x); 
 a := selectfun(func, ln); 
 `assuming`([simplify(eval(func, [seq(a[k] = map(proc (x) options operator, arrow; 
 abs(x) end proc, a[k]), k = 1 .. nops(a))]))], [x in real]) end proc:

 REALINT2(1+1/x, x); 
 REALINT2(1/sin(x), x); 
 REALINT2(x/(x^2+1), x); 
 REALINT2(tan(x), x); 
 REALINT2((diff(f(x), x))/f(x), x); 
 REALINT2(1+1/abs(x), x); 
 `assuming`([REALINT2(1/x, x)], [x < 0])

 #                          x + ln(|x|)
 #                 ln(1 - cos(x)) - ln(|sin(x)|)
 #                          1   / 2    \
 #                          - ln\x  + 1/
 #                          2           
 #                         -ln(|cos(x)|)
 #                           ln(|f(x)|)
 #                     / x - ln(-x)      x < 0
 #                    |                      
 #                    <  undefined       x = 0
 #                    |                      
 #                     \ x + ln(x)       0 < x
 #                             ln(-x)