Inconsistent results from "int" function

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YoungJoo Lee
YoungJoo Lee 2022-11-27
评论： YoungJoo Lee 2022-11-27
Hi, everyone. For the same question, the "int" function provided me with different results.
syms x y
int(x*y/24+y^2/48,x)
int((y*(2*x + y))/48,x)
The second line gave me "(x*y*(x + y))/48" which was what I originally wanted,
but the third line gave me "'(y*(2*x + y)^2)/192" which is wrong.
Can anyone explain the reason?
Thanks for your time and help in advance!

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Alan Stevens
Alan Stevens 2022-11-27
You can express '(y*(2*x + y)^2)/192 as (x*y*(x + y))/48+y^3/198
As far as the integral is concerned y is a constant, so the two results are the same to within a constant, which is all you can guarantee from an integral with no specific limits.
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Torsten
Torsten 2022-11-27
I believe, for my problem, providing something like "(x*y*(x + y))/48+C (where C is a constant)" as output would be more appropriate.
"(x*y*(x + y))/48+C(y) (where C is a function solely depending on y)"

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