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  • Strange result by FriCAS on this integral.

    From Nasser M. Abbasi@21:1/5 to All on Fri May 14 01:56:22 2021
    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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  • From [email protected]@21:1/5 to Nasser M. Abbasi on Sat May 15 13:13:08 2021
    Nasser M. Abbasi <[email protected]> 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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