As it has appeared recently, in some examples Maple can't find int(1+f(x), x) in some cases where it can find int(f(x), x). For example, for f(x) = (x^2)^(1/3).

Now, reading Axel Vogt's post, I noticed that in some examples Maple can't do such a simple change of variables as changing the sign.

J:=Int(exp(-eta^2+eta)/(1+exp(eta)),eta = -infinity .. infinity);
                        infinity
                       /                 2
                      |          exp(-eta  + eta)
                J :=  |          ---------------- deta
                      |            1 + exp(eta)
                     /
                       -infinity

value(J);

                     infinity
                    /                 2
                   |          exp(-eta  + eta)
                   |          ---------------- deta
                   |            1 + exp(eta)
                  /
                    -infinity

Changing the sign manually also has appeared to be not such a simple operation as it may seem,

J1:=IntegrationTools:-Change(J,eta=-theta);
                   infinity
                  /
                 |            exp(-theta (theta + 1))
         J1 := - |          - ----------------------- dtheta
                 |                1 + exp(-theta)
                /
                  -infinity
value(J1);
                infinity
               /
              |            exp(-theta (theta + 1))
            - |          - ----------------------- dtheta
              |                1 + exp(-theta)
             /
               -infinity

Even double minus signs didn't get cancelled! It took me some time to find the correct simplification steps,

J1:=simplify(IntegrationTools:-Expand(J1));
                        infinity
                       /                    2
                      |           exp(-theta )
               J1 :=  |          -------------- dtheta
                      |          exp(theta) + 1
                     /
                       -infinity

value(J1);

                                  1/2
                                Pi
                                -----
                                  2

Shouldn't it be more simple than that?

Alec