@Alejandro Jakubi

How does Mathematica integrate this equation?
(Sorry, I don't have Mathematica to try)

And, according to your disscussion, whether can I get the correct result if I make some assumption or definition in Maple? For example, I assume ln(0) = -infinity (if Maple can do this) and get the result " undefined if -100<n<-10, -ln|n+10|+ln|n+100| otherwise".

Or, I define some properties of parameters in the integral to make command int get the correct piecewise function?

Obviously, the option you use in command solve cannot to be used in command int. How to do this kind of assumption? I know the command asuume, but it seems that assume cannot do this job.

Thank you all :)

@Markiyan Hirnyk Thank you for your help :)

@Preben Alsholm 

Thanks for your information, anyway.

@Carl Love 

Oh, so that's how it is. Thanks.

@Carl Love 

Thank you for your answer. Very detailed. 

But for the first part, do you know the purpose of function "In-place operation"? Why the command Map want to change its arguments. It must to benefit some computation which I don't know about.

@Carl Love 

I only want to express the result is beyond my expectation, thanks, anyway.

@mehdi jafari 

OK!! I see!!

Thank you very very much~

@Carl Love 

Thanks for your suggestion, I did notice another inconsistency:

T____T

@Preben Alsholm 

What I confused is the fifth action of Maple in this example.

Why the map printed five outputs but accepted only four operands from the list (or vector)?

@mehdi jafari 

So... do you mean the "[]" is not the operands from an expression?

@Carl Love 

Thank you Carl~

@Carl Love 

Thank you for your answer. And I attached the file again.

@Alejandro Jakubi 

That's cool. It's the first time I've heard of such a special method.

Thank you~ :)

@Carl Love

Thanks for your opinion.

It's a very conveninet way that I've never thought of before.

<v> uses the vector v being a unit of the new vector and it's no doubt that it creates a matrix.

But "m[...,1]"...  It means the part of the matrix is not another matrix absolutely, for example:

m:=Matrix(3,1,[x,y,z]):

m1:=m[1..3,1]:

m2:=m[1..3,1..1]:

lprint(m1)

Vector[column](3, {1 = x, 2 = y, 3 = z}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])

lprint(m2)

Matrix(3, 1, {(1, 1) = x, (2, 1) = y, (3, 1) = z}, datatype = anything, storage = rectangular, order = Fortran_order, shape = [])

It's the other very interesting topic. Thank you.

@Axel Vogt

Thank you for reminding me.

In some cases, it makes no sense to compute the mapping matrix and the vector space.

Ok, it works now. Thank you for your kindly help :D