I had to use integration by parts to get the answer I need, but I do not think it is really needed for this. compare the output from:

r:=int(tan(x)^(n-2)*sec(x)^2,x);

(which is pages of very complicated output), with this:

r:=Int(tan(x)^(n-2)*sec(x)^2,x):
simplify(value(IntegrationTools:-Parts(r,tan(x))));

Does one really have to tell Maple to do integration by parts for this? I would have expected int() to do it as is.

Please compare to Mathematica:

Maple 18.02

added

The reason I think this should have been done by int() directly is that it is direct  application of the power rule of integration. I can't write Latex here, so I wrote it on my computer, and I copy the screen shot to explain for those interested:

Maple is so good in differential equations, but does not seem to be as good as it should when it comes to integration.

2 questions: How would one delete  an execution group that is at top of a work sheet? Like this:

No matter what I do, I get a beep. I select it, click DELETE and nothing happens.

THe second question, is how to delete the last section arrow I added by mistake and do not want, this one:

I found I can remove if I select it with the line above, but then that would delete the code above also, which I'd like to keep.

Why is so awkward to use Maple user interface like this? Is this by design?

To make it easier, I attach the above notebook.

hard_to_delete.mw

I prefer to write packge:-command(....) so I can see which package the command is from.

But sometimes I am forced to load  a package. Here is an example. IntegrationTools contains some useful types

At load time the IntegrationTools package defines three new types: Integral, DefiniteIntegral and IndefiniteIntegral, which can be used to access integrals involved in any given expression.

I thought I can access these just like the commands in the package, using ":-" notation, but this does not work

------------------
restart;
v := Int(sin(x), x);
type(v,IntegrationTools:-IndefiniteIntegral);
---------------------

Error, IndefiniteIntegral is not a command in the IntegrationTools package

But this works

-----------------------
restart;
with(IntegrationTools);
v := Int(sin(x), x);
type(v,IndefiniteIntegral);
----------------

It looks like :- only works to access functions/commands/procs in a package. and not to access types such as in this example.

Is there some other notation to use to reference types in package without having to load the whole package?

according to help on Combine

The Combine command combines integrals using linearity. The parameter v is any expression involving definite or indefinite integrals.

So, why I get an error from the following?

restart;
expr:=Int(sin(x),x) + Int(cos(x),x);

IntegrationTools:-Combine(expr);

Error, (in IntegrationTools:-Combine) invalid subscript selector

interface(version);
 Standard Worksheet Interface, Maple 18.02, Windows 7, October  20 2014

I am trying to learn the <> notation to enter matrices and vectors. But I find this page very confusing

http://www.maplesoft.com/support/help/maple/view.aspx?path=examples%2FLA_Syntax_Shortcuts

it says:

but we see clearly the vertical bars are used to separate columns.

Isn't a column the thing that goes from the top to bottom and not from left to right in Maple LinearAlgebra?