Why FriCAS gives zero on this integral?

FriCAS Computer Algebra System
Version: FriCAS 1.3.6
Timestamp: Mon 09 Mar 2020 12:35:03 PM CDT

(1) -> integrate(cos(x)*cos(2*x)*sin(3*x)/(-5+4*sin(x)^2)^(5/2),x)

(1) 0

This is #425 in Timofeev test suite. No error or any other message is given.

<https://www.12000.org/my_notes/CAS_integration_tests/reports/rubi_4_16_1_graded/test_cases/0_Independent_test_suites/Timofeev_Problems/rese425.htm#x429-4510003.425>

The optimal anti according to Rubi's input files is

-1/(4*(-5 + 4*Sin[x]^2)^(3/2)) - 5/(8*Sqrt[-5 + 4*Sin[x]^2]) + Sqrt[-5 + 4*Sin[x]^2]/8


--Nasser

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Nasser M. Abbasi <nma@12000.org> wrote:

Why FriCAS gives zero on this integral?

FriCAS Computer Algebra System
Version: FriCAS 1.3.6
Timestamp: Mon 09 Mar 2020 12:35:03 PM CDT

(1) -> integrate(cos(x)*cos(2*x)*sin(3*x)/(-5+4*sin(x)^2)^(5/2),x)

(1) 0

This is #425 in Timofeev test suite. No error or any other message is given.

Looks like a bug. Note that integral is written as real thing, but
expression under square root is always negative on real axis, AFAICS
this triggers bug.

--
Waldek Hebisch

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