Antiderivatives

User login

Poll

What is this?

Posted on 2008-07-20 20:30 By KewlEugene (

15)

Categories:

How do I ...? with Maple (Student)

Hi,

This is my 1st try with Antiderivatiives using Maple 12 Student Edition. These statements work fine and the answers are the same as the book.

int(15*x^4-cos(x)+5, x);
int(8*x^3+Pi*cos(Pi*x), x);

but the below doesn't work. Maple just repeats it with the Integral symbol before it and 'dx' after it. by hand the answer is 3x^(5/3)+x^(3/5)+C.

int(5*(x^2)^(1/3)+3/(5*(x^2)^(1/5)), x);

thanks

gaah !

Comment on 2008-07-20 21:04 from KewlEugene (

15)

gaah ! is that all it was ?

i typed in the graphical radical symbol from the 'Expression' left bar, it doesn't show on the original post. so the 'int' statement doesn't like it's own Maple input ?

in any case, thanks for clearing that up for me.

The Maple language

Comment on 2008-07-20 23:01 from JacquesC ( Maple Rating 4

1629)

The Maple kernel and library understand the ASCII Maple language just fine. However, there are a whole bunch of oddities with the "graphical" version, which makes it look like Maple doesn't understand its own input. Until those bugs are fixed, it is safest to use 1D input (see the Options menu).

Adding 1 to the integrand

Comment on 2008-07-21 02:02 from alec ( Maple Rating 4

1443)

Maple is not able to do the original integral even in the Classic Interface.

Here is another example, more simple, that Maple has problems with,

int(1+(x^2)^(1/3),x);
                           /
                          |        2 (1/3)
                          |  1 + (x )      dx
                          |
                         /

Without adding 1, it works OK,

int((x^2)^(1/3),x);
                                   2 (1/3)
                           3/5 x (x )

Alec

different paths

Comment on 2008-07-21 02:16 from jakubi ( Maple Rating 4

665)

Tracing a bit with

infolevel[all]:=3:
trace(int):

I see that the computation paths with and without 1 are very different. Eg, without, it goes to:

PolynomialNormalForm:   "construct the differential polynomial normal form"

When did it start?

Comment on 2008-07-21 14:09 from alec ( Maple Rating 4

1443)

It looks like an obvious thing to do - if an integrand is a sum of 2 terms, integrate each of them and then add.

Did this problem start in Maple 12 or earlier?

Alec

Since Maple 9.5

Comment on 2008-07-21 14:54 from jakubi ( Maple Rating 4

665)

this split in computational paths occurs (more precisely I have checked Maple 9.52).

With Maple 9.03:

int((x^2)^(1/3),x);

goes through Risch integration and produces:

yes

Comment on 2008-07-21 15:26 from Axel Vogt ( Maple Rating 4

866)

it needs

  int(1+(x^2)^(1/3),x); expand(%);
                                     2 (1/3)
                         x + 3/5 x (x )

to get the result

}