On 6/15/2022 11:21 PM, Nasser M. Abbasi wrote:

Btw, the above integrals is from Rubi's test suite. Here is last years output:

<https://www.12000.org/my_notes/CAS_integration_tests/reports/summer_2021/test_cases/4_Trig_functions/4.1_Sine/4.1.2.2-g_cos-%5Ep-a+b_sin-%5Em-c+d_sin-%5En/rese158.htm#x162-1860003.158>

Opps. Wrong link. Here is the correct integral

<https://www.12000.org/my_notes/CAS_integration_tests/reports/summer_2021/test_cases/4_Trig_functions/4.1_Sine/4.1.1.2-g_cos-%5Ep-a+b_sin-%5Em/rese158.htm#x162-1860003.158>

I see that giac last year version (1.7 version) that it generated much
shorter output for this same integral (using sagemath interface)

----------------------------

integrate(cos(d*x+c)^5/(a+a*sin(d*x+c))^(1/2),x, algorithm="giac")


2/315*(107*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (315*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (324*a^4/sgn(tan(1/2*d
*x + 1/2*c) + 1) + (420*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (882*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (882*a^4/
sgn(tan(1/2*d*x + 1/2*c) + 1) + (420*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1) + (324*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1
) + (107*a^4*tan(1/2*d*x + 1/2*c)/sgn(tan(1/2*d*x + 1/2*c) + 1) + 315*a^4/sgn(tan(1/2*d*x + 1/2*c) + 1))*tan(1
/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1
/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))*tan(1/2*d*x + 1/2*c))/((a*tan(1/2*d*x + 1/2*c)^2 + a)^(9/2)*d)
--------------------------------

It is possible then this could be a new bug in giac. I will report it now
just in case.

--Nasser

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