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Question: Unable to reduce these (specific) primitive functions to rational, arctan and ln?

Question:Unable to reduce these (specific) primitive functions to rational, arctan and ln?

sursumCorda 1079 Maple 2023
integration simplify int simplification indefinite spelling
May 03 2023
1

In accordance with this statement obtained by Чебышёв (1853), each of 

simplify(int(x^(1/2)*(x^2 + 1)^(-3/4), x), symbolic);
simplify(int((x^(1)*(1 - x^2))^(1/3), x), symnolic);
simplify(int(x^(-1)*(x^6 + 1)^(-1/6), x), symnolic);
simplify(int(x^(17/2)*(x^2 + 1)^(1/4), x), symnolic);

can be reduced to an integral of rational functions, which can be expressed in terms of elementary functions. But it appears that Maple 2023.0 is still unable to completely calculate them. For instance: 
 

> 

restart;
> 

interface(version)

`Standard Worksheet Interface, Maple 2023.0, Windows 10, March 6 2023 Build ID 1689885`

 (1)
> 

timelimit(0.1e4, `assuming`([simplify(int(x^(1/2)/(x^2+1)^(3/4), x))], [x > 0]))

(2/3)*x^(3/2)*hypergeom([3/4, 3/4], [7/4], -x^2)

 (2)
> 

timelimit(0.1e4, `assuming`([simplify(int((x*(-x^2+1))^(1/3), x))], [`or`(`and`(x <= 1, x >= 0), x <= -1)]))

(3/4)*x^(4/3)*hypergeom([-1/3, 2/3], [5/3], x^2)

 (3)
> 

timelimit(0.1e4, `assuming`([simplify(int(1/(x*(x^6+1)^(1/6)), x))], [x <> 0]))

-(1/36)*x^6*hypergeom([1, 1, 7/6], [2, 2], -x^6)-(1/12)*Pi*3^(1/2)-(1/3)*ln(2)-(1/4)*ln(3)+ln(x)

 (4)
> 

timelimit(0.1e4, `assuming`([simplify(int(x^(17/2)*(x^2+1)^(1/4), x))], [x > 0]))

(1/81920)*(8192*x^10*(x^2+1)^(1/4)+512*x^8*(x^2+1)^(1/4)-640*x^6*(x^2+1)^(1/4)+880*x^4*(x^2+1)^(1/4)-1155*ln(2*RootOf(_Z^2+1)*x^(1/2)*(x^2+1)^(3/4)-2*RootOf(_Z^2+1)*x^(3/2)*(x^2+1)^(1/4)+2*(x^2+1)^(1/2)*x-2*x^2-1)*x^(1/2)*RootOf(_Z^2+1)-1540*x^2*(x^2+1)^(1/4)-1155*x^(1/2)*ln(-2*x^(1/2)*(x^2+1)^(3/4)-2*x^(3/2)*(x^2+1)^(1/4)+2*(x^2+1)^(1/2)*x+2*x^2+1))/x^(1/2)

 (5)
> 

gc()


 

Download Chebyshev_theorem_on_the_integration_of_binomial_differentials.mws

However, closed-form (and readable) solutions in elementary forms exist (cf. Regression reports for Computer Algebra Independent Integration Tests. Summer 2022 version (12000.org)); in fact, Mathematica returns: 

So, why can't Maple find these compact antiderivatives (expressed by elementary functions) directly here? In other words, is there a way to resolve them in Maple without applying some change of the variable to these indefinite integrals manually?
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