@Kitonum 

You are right, but for some reasons I would like to force Maple to work properly........

@Kitonum 

Thank you for advise, but, to my mind, the simplest way is the use of abacus istead of computer (it's a joke, don't be offended).

@ 

Thank you, now I'm aware of this approach.

@Carl Love 

Thank you, Carl. Indeed, Digits = 15 is a threshold for described issue. I would like to know, if it is possible to increase the precision of dsolve's solution in order to calculate integrals with higher precision (Digits > 15)?

@Carl Love 

Having tryed all ways above, I see, that the simplest method for calculation of integrals of powers of procedures (u^a) is to write own procedure of numerical integration based on some integration scheme with control of precision and convergence.

@Carl Love 

Here the result of second workaround:

It is a true curse!

@Carl Love 

18.02

@Carl Love 

Dear Carl, integration of u² does not work:

@Axel Vogt 

Thank you, Axel. Es funktioniert.

@Rouben Rostamian  

Thank you. Certainly, It’s a simple straightforward way and if it is not possible to calculate derivative of proc explicitly, it can be used.

@Preben Alsholm 

Of cause, dsolve returns the derivative of solution , I know this:

But I need to calculate the derivative of second order of solution ().

Is it possible?

@Carl Love 

Thank you for reply, I guessed that Matrices/Vectors are handled in special way in Maple sets.

Regards

Thank you for reply. Your custom procedure uses the cycle through all permutations of rows and  columns and for large m, n, m1, n1 can be computationally intensive. I meant more optimised algorithm suitable for large-sized matrices.
Nevertheless I am very much obliged to you for your fast answer.

So I have a normal vision, the font in some interface elements of Maple looks annoying. Say I would like to have bigger font in Find dialogue:

@Carl Love 

Many thanks. It's a thing I searched for. For some reasons I didn't notice Canonicalize function earlier in Lgic package.