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Let us consider 

J := int(x^n/sqrt(1+x^n), x = 0 .. 1) assuming n > 0;

2*(2^(1/2)-hypergeom([1/2, 1/n], [(n+1)/n], -1))/(2+n)

limit(J,n=infinity);
FAIL
MultiSeries:-limit(J,n=infinity);
FAIL

Mma 11 finds the limit is zero. Hope one feels the difference.
limit mma

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