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Question: integrals in Maple

Question:integrals in Maple

J F Ogilvie 258 Maple
integration
January 12 2011
0

int(sqrt(1 + sec(x)^2), x)

int(sqrt(2 + tan(x)^2), x)

With Maple 13, which is the latest version on the computer on which I tested these integrals (that originated with a

senior scientist in Australia), the former yields a reasonably compact answer, but the latter yields an extensive

output containing Elliptic functions of various kinds.  The two integrands are trigonometric identities.  What is the

problem here?

     Incidentallly, Mathematica 8 yields only the former compact result, and instantly, in both cases.
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