Why Maple likes to extract exp() outside the sqrt when its argument has minus sign vs. not?  Compare the following

restart;
eq2 := ln(2*u^2 + u - 1) = -c - 2*ln(x);
sol:=[solve(eq2,u)]:
simplify(sol[1])

and

eq2 := ln(2*u^2 + u - 1) = c - 2*ln(x);
sol:=[solve(eq2,u)]:
simplify(sol[1])

I like the above much better than the first one. Mathematica keeps both same form (i.e. keeps the exp() inside):

Maple's answers are correct ofcourse, I just do not understand the logic why when there is a minus sign on c it likes to format it differently as shown.

Is there a way to make not do that?

In Maple 2021.1

restart;
int(cos(3*x)/(-(-1+8*cos(x)^2)^(1/2)+(3*cos(x)^2-sin(x)^2)^(1/2)),x)

gives

Error, (in SumTools:-DefiniteSum:-ClosedForm) numeric exception: division by zero

But in Maple 2020.2 it works OK giving an answer. (A very long one)

btw, the answer should be

3/4*arcsin(2/3*sin(x)*3^(1/2))-3/4*arctan(sin(x)/(-1+4*cos(x)^2)^(1/2))-3/4*arctan(sin(x)/(-1+8*cos(x)^2)^(1/2
))+5/8*arcsin(2/7*sin(x)*14^(1/2))*2^(1/2)-1/2*sin(x)*(-1+4*cos(x)^2)^(1/2)-1/2*sin(x)*(-1+8*cos(x)^2)^(1/2)

Is this a known issue? I know Maple int has went some changes and improvements in Maple 2021 from the release notes. May be this was caused by some of these changes?

https://www.maplesoft.com/products/maple/new_features/

• Integration has been enhanced with improved algorithms for indefinite integration, and the ability to easily specify which integration method should be used and to compare the results from different methods."

Maple 2021.1 on windows 10

update July 2, 2021

These are additional failed integration in 2021.1 that throw exceptions now. no errors in 2020.2

#427
int(cos(3*x)/(-(-1+8*cos(x)^2)^(1/2)+(3*cos(x)^2-sin(x)^2)^(1/2)),x)

#533 #no error in Maple 2020, it does not evaluate there. But no error
int((-3+exp(7*x))^(2/3)/exp(2*x),x)

#26/11 #no error in Maple 2020, it does not evaluate there. But no error
int((b*x+(b^2*x^2+a)^(1/2))^(1/2)/(b^2*x^2+a)^(1/2),x)

dsolve accept system of first order ode's in the form x'=A x, where x' is vector, A is matrix of coefficients and x are the dependent variables. This is convenient since one does not have to convert things to a list.

But  dfieldplot and phaseportrait and DEplot do not accept this form. One must convert things to list first.

Here is an example

restart;
sys:=Vector([diff(x(t),t),diff(y(t),t)]) = Matrix([[1,2],[0,3]]).Vector([x(t),y(t)]);
dsolve(sys)

But

DEtools:-dfieldplot(sys,[x(t),y(t)],t=0..4,x=-4..4, y=-4..4);

Error, (in DEtools/dfieldplot) system must have same number of dependent variables as DE's.

workaround is to write the system as list

new_sys:=[diff(x(t), t)=x(t) + 2*y(t),diff(y(t), t)=3*y(t)];
DEtools:-dfieldplot(new_sys,[x(t),y(t)],t=0..4,x=-4..4, y=-4..4);

I know one can automate the conversion. But still, it would be better if dfieldplot would accept sys as dsolve did.

Same for 

DEtools:-phaseportrait(sys,[x(t),y(t)],t=0..4,[[x(0)=1,y(0)=0]],x=-4..4, y=-4..4);
#
DEtools:-DEplot(sys,[x(t),y(t)],t=0..4,[[x(0)=1,y(0)=0]],x=-4..4, y=-4..4);

They gives same error.

Since dsolve can do it, may be these other functions can also support taking a system of ode's in vector/matrix form? Any reason why not?

Maple 2021.1

I do not remember if there was a post on this before or not
Maple 2021.1

int(arcsin(x)/(1+(-x^2+1)^(1/2)),x)

gives

Error, (in Utils:-TransformAndApply) numeric exception: division by zero

The correct answer should be

((-1 + Sqrt[1 - x^2]) ArcSin[x])/x + ArcSin[x]^2/2 -  Log[1 + Sqrt[1 - x^2]]

I had to go back to Maple 2018, to get no exception:

May be this could be looked at for next Maple version?

I have plain text file generated, where each line has mixed numbers and strings. Some of the strings are latex. So they have "\" in them. The data is rectangle. same number of fields on each line, separated by commas.  I use CSV format to read the data to Maple.

I simply want to read this file using Import , which reads it into a matrix (using CSV format), and export it back right away using either ExportMatrix or Export and end up with the same exact file.

But Maple always adds extra "\" each time I export the matrix back to the file. So if I have initially "\sin x" in the file, after reading/writing the file 5 times without touching the data inside Maple, I end up with something like "\\\\\\\\\\\sin x" in the file at the end.

I could ofcourse not use ExportMatrix nor Export and write the data back to the file manually using fprintf using correct format for each field. But it is easier if I can get ExportMatrix to work since there are many fields some are integers, some are real and some are strings.

Here is a simple MWE which shows the problem. Originally I have this file on disk. Called test.txt and has 2 lines in it

1,"\sin x"
2,"this is second line"

Now after doing the following

data:=Import("test.txt",format="CSV",output=Matrix):  
ExportMatrix("test.txt",data,target=csv);

The file on disk now becomes

1,"\\sin x"
2,"this is second line"

And repeating the above one more time, the file becomes

1,"\\\\sin x"
2,"this is second line"

This ofcourse breaks all the latex strings in there.

Is there a way to prevent Maple from doing this? I looked at all the options in help, but do not see on so far.  I also tried Export but that did not work at all. So I'd like to see if ExportMatrix can do it, without adding an extra "\", otherwise, will have to use fprintf directly to export the data back to file.

edit

fyi, I ended up using fprintf to write the data back to disk. May be if there is a solution using ExportMatrix, will change back. This is what I ended up doing

File before

1,"\sin x"
2,"this is second line"

Now run this code

data:=Import("test.txt",format="CSV",output=Matrix):  
file_id := fopen("test.txt",WRITE):
nRows:=LinearAlgebra:-RowDimension(data);
for n to nRows do
    if n<nRows then
       fprintf(file_id,"%d,\"%s\"\n",data[n,1],data[n,2]);
    else
       fprintf(file_id,"%d,\"%s\"",data[n,1],data[n,2]);
    fi;
od;
fclose(file_id);

File after

1,"\sin x"
2,"this is second line"

Now the file is exactly the same as before reading it.

My actual data is more than the above two fields, but that makes the format string longer, that is all.