Incredible symbolic integration problems

Guys, I have incredible integration issues, see below:

I need to calculate a difficult integral and I didn't obtain good results, so I try a very simple integral in order to try to understand the problem and as you can see from the code below, Matlab provides a wrong results, beacuse the correct results is (-log(1-x)) and not (-log(x-1)), and for these reasons I'm having lots of troubles in my computations. Honestly, I have no idea about this problem, I even doubts about my capabilty of calculating such a simple integral so that I verify with WolphramAlpha that provides the correct results!

Could someone help me? Thank you very much and sorry for my english.

>> int ((-1./(1-x), x)
ans = 
-log(x-1)

[Giuseppe Infantino]

Thanks, I'm using 9.4.0.813654 R2018a version

Answer 1

[Star Strider]

It looks correct to me.

The int call first simplifies:

-1/(1-x)

to:

1/(x-1)

and then integrates it to get:

Q1 = int (-1./(1-x), x)

producing:

Q1 =
log(x - 1)

The unary negative does not propagate when I run it in R2019b.

[Giuseppe Infantino]

yes you're right, but now I am a bit confused. Actually if i try to compute int (1/(1-x), x) , Matlab gives me -log(x-1), but even if 1/(1-x) is equal to -1/(x-1) , when the integral is computed i need the version log(1-x) because my domain x belongs to [-1,1]...

Sorry If this could appear a very ridicoulous problem, but how I can solve ? How I can get the expression log(1-x) ?

[Star Strider]

MATLAB appears to view them as being interchangable:

syms x 
Q1 = diff(log(1-x),x)
Q2 = int(Q1,x)

producing:

Q1 =
1/(x - 1)

Q2 =
log(x - 1)

I cannot find any name-value pair arguments in the int function that would not result in its interim simplification. That is just how the Symbolic Math Toolbox orders expressions.

[Giuseppe Infantino]

so you're saying to me that it's impossible with the intengration in matlab to obtain the results log(1-x)? There is absolutely no way?

[Walter Roberson]

There is absolutely no way?

I would not say that there is absolutely no way, but I would say that it might take someone outside of Mathworks... 2 or 3 person-years at least. It would involve a fundamental change to the simplification algorithm, and there is a whole bunch of existing mathematical library code that counts on the algorithm being what it currently is, so it would take a careful review of every routine inside the Symbolic Toolbox to ensure that they did not break.

It would be a lot faster if you were willing to adapt a different syntax, such as

int( DIVIDE(-1, 1-x), x)

because that could be implemented as a new data structure that only had to be processed by a limited number of routines, with it just being expected that (for example) GAMMA() could not be called on the result

[Star Strider]

@Walter — Thank you!