It may happen if you used = sign in the definition of u, instead of := .

Or, it may be a different Maple version - I did that in Maple 12.

Alec

It may happen if you used = sign in the definition of u, instead of := .

Or, it may be a different Maple version - I did that in Maple 12.

Alec

I did it in Classic Maple. Copying and pasting should work there. The important thing is that the first letter in int should be small (i.e. not Int). Also, you might try to restart (i.e type restart; ) before assigning u and doing the integrals in case if some of the variables were assigned.

Alec

I did it in Classic Maple. Copying and pasting should work there. The important thing is that the first letter in int should be small (i.e. not Int). Also, you might try to restart (i.e type restart; ) before assigning u and doing the integrals in case if some of the variables were assigned.

Alec

In Standard Maple, that can be done by using context menu. Enter the function, move the mouse pointer over it and click the right mouse button, scroll down to Differentiate, and click on x. Don't enter y and =, just the expression of x. Also, don't forget to put a multiplication sign between two parentheses in the first example, and don't forget to add parentheses around (3x-1/x) in the second example (if it is the square root of that; if it is the square root of 3x, just add parentheses around 3x).

Alec

While

expand(Int(f(x)-g(x),x));
                        /             /
                       |             |
                       |  f(x) dx -  |  g(x) dx
                       |             |
                      /             /

it is interesting that

expand(Int(1/(x-1)-1/x,x));
                             /
                            |      1
                            |  --------- dx
                            |  (x - 1) x
                           /

In what sense that may be called expanding?

It works similarly for sums,

expand(Sum(1/(x-1)-1/x,x=2..n));
                             n
                           -----
                            \        1
                             )   ---------
                            /    (x - 1) x
                           -----
                           x = 2

Alec

While

expand(Int(f(x)-g(x),x));
                        /             /
                       |             |
                       |  f(x) dx -  |  g(x) dx
                       |             |
                      /             /

it is interesting that

expand(Int(1/(x-1)-1/x,x));
                             /
                            |      1
                            |  --------- dx
                            |  (x - 1) x
                           /

In what sense that may be called expanding?

It works similarly for sums,

expand(Sum(1/(x-1)-1/x,x=2..n));
                             n
                           -----
                            \        1
                             )   ---------
                            /    (x - 1) x
                           -----
                           x = 2

Alec

I meant the case of indefinite integrals,

v := Int(s*f(x)+t*g(x), x);

                            /
                           |
                     v :=  |  s f(x) + t g(x) dx
                           |
                          /

expand(v);

                        /               /
                       |               |
                    s  |  f(x) dx + t  |  g(x) dx
                       |               |
                      /               /

Actually, that may be wrong for integrals, if f(x) and/or g(x) are not integrable, so that, maybe, shouldn't work like that, in general. The same for infinite sums - such expanding also may be wrong. There seem to be no such a problem for finite sums.

Alec

I meant the case of indefinite integrals,

v := Int(s*f(x)+t*g(x), x);

                            /
                           |
                     v :=  |  s f(x) + t g(x) dx
                           |
                          /

expand(v);

                        /               /
                       |               |
                    s  |  f(x) dx + t  |  g(x) dx
                       |               |
                      /               /

Actually, that may be wrong for integrals, if f(x) and/or g(x) are not integrable, so that, maybe, shouldn't work like that, in general. The same for infinite sums - such expanding also may be wrong. There seem to be no such a problem for finite sums.

Alec

Alejandro,

That, by the way, gives another way of doing that, not so cryptic as with map and op,

S:=Sum((A*x[i]+B)^2, i = 1 .. n): 

eval(IntegrationTools:-Expand(eval(S,Sum=Int)),Int=sum);

                /  n        \         /  n       \
                |-----      |         |-----     |
              2 | \        2|         | \        |      2
             A  |  )   x[i] | + 2 A B |  )   x[i]| + n B
                | /         |         | /        |
                |-----      |         |-----     |
                \i = 1      /         \i = 1     /

Alec

Alejandro,

That, by the way, gives another way of doing that, not so cryptic as with map and op,

S:=Sum((A*x[i]+B)^2, i = 1 .. n): 

eval(IntegrationTools:-Expand(eval(S,Sum=Int)),Int=sum);

                /  n        \         /  n       \
                |-----      |         |-----     |
              2 | \        2|         | \        |      2
             A  |  )   x[i] | + 2 A B |  )   x[i]| + n B
                | /         |         | /        |
                |-----      |         |-----     |
                \i = 1      /         \i = 1     /

Alec

There is a SumTools package (which is quite good, by the way - I would say _unusually_  good), but it goes in the different direction than IntegrationTools. The Student:-Calculus1 package has Summand command which shows that it was planned originally to include Sum problems in the Step-by-Step procedures with Rule and Hint, analogous to Int. However, that was not done, and Summand stands alone there without much of use.

The problem here, I think, is not in student or Student packages, but in expand. It should work for sums the same way as it works for integrals - then it could be done as in Axel Vogt's posts in this thread.

Alec

There is a SumTools package (which is quite good, by the way - I would say _unusually_  good), but it goes in the different direction than IntegrationTools. The Student:-Calculus1 package has Summand command which shows that it was planned originally to include Sum problems in the Step-by-Step procedures with Rule and Hint, analogous to Int. However, that was not done, and Summand stands alone there without much of use.

The problem here, I think, is not in student or Student packages, but in expand. It should work for sums the same way as it works for integrals - then it could be done as in Axel Vogt's posts in this thread.

Alec

It seems as if none of those wishes were implemented in Maple 12, except KroneckerProduct which was implemented before that wish-list started.

Alec

There are 2 other things in that which could be considered as bugs as well, beside a poor display.

First - 8^(1/3) shouldn't appear in the display at all, it should be evaluated to 2, then multipled by 8 and the result should be displayed as 16.

Second - if it is displayed, it should be displayed as the cube root of 8 and not as 8 in the power 1/3.

Alec