## 630 Reputation

19 years, 288 days

## Int(ln(1+x)/(1+x^2),x=0..1)...

Maple

Maple evaluates

Int(ln(1+x)/(1+x^2),x=0..1);

as

1/2*I*dilog(1/2+1/2*I)-1/2*I*dilog(1/2-1/2*I)+1/4*Pi*ln(2)-Catalan

It would be nice if Maple could simplify this to 1/8*Pi*ln(2). If you evalf the integral and use "identify" then Maple does return 1/8*Pi*ln(2).

MMa directly returns 1/8*Pi*ln(2), which seems preferable.

## integration problem...

Maple

It's frustrating that Maple 14 evaluates this integral to be 0:

int(sqrt(-8*cos(t)*sin(t)+5),t=0..2*Pi);

( The integrand is positive over the interval.)

This equivalent integral is evaluated correctly in terms of EllipticE:

int(sqrt(-4*sin(2*t)+5),t=0..2*Pi);

## Matrix problem...

Maple

I have an Nx3 Matrix A and each row looks like [integer,integer,*]. Matrix A acts like a function of two variables in the sense that the ordered pairs that you get be selecting the first two entries of each row are all distinct.

I would like a slick way to convert A to a Matrix B for which B[i,j]=* where * is the third entry in the unique row of A that looks like [i,j,*]. We can insert 0 for "blanks."

For example, if

A:=Matrix([[1,3,a],[1,4,d],[1,1,b],[3,3,c],[3,4,a]])

1 3 a
1 4 d
1 1 b

## sorting...

Maple

I have a list of coordinates  and would like to sort them so that in the new order, the third coordinate is increasing.

For example,

data:=[ [2,3,1], [3,6,-1], [5,0,3] ]

should sort to

[ [3,6,-1], [2,3,1], [5,0,3] ]

There must be an intelligent way to do this.

## output numeric format...

Maple

In Classic, this input:

753406.29+42098.70;

yields this output:

795504.99

But in Standard, the same input yields

7.9550499 10

How do I set my options in Standard so that the output format is like it is in Classic?

I poked around "display options" etc. but did not find anything.

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