Integrals 1001 to 1071

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2.2.11 Integrals 1001 to 1071

Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.

In this table, the column N.S. means normalized size and is deﬁned as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table ﬁt the page, the name Mathematica was abbreviated to MMA


Problem 1001	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	58	58	56	0	0	0	44	0	0
N.S.	1	1.00	0.97	0.00	0.00	0.00	0.76	0.00	0.00
time (sec)	N/A	0.171	10.014	0.000	0.000	0.000	0.739	0.000	0.000


Problem 1002	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	56	56	54	0	0	0	44	0	0
N.S.	1	1.00	0.96	0.00	0.00	0.00	0.79	0.00	0.00
time (sec)	N/A	0.171	10.012	0.000	0.000	0.000	1.025	0.000	0.000


Problem 1003	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	56	56	54	0	0	0	48	0	0
N.S.	1	1.00	0.96	0.00	0.00	0.00	0.86	0.00	0.00
time (sec)	N/A	0.170	10.012	0.000	0.000	0.000	1.838	0.000	0.000


Problem 1004	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	61	61	59	0	0	0	44	0	0
N.S.	1	1.00	0.97	0.00	0.00	0.00	0.72	0.00	0.00
time (sec)	N/A	0.170	10.020	0.000	0.000	0.000	12.636	0.000	0.000


Problem 1005	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	61	61	59	0	0	0	44	0	0
N.S.	1	1.00	0.97	0.00	0.00	0.00	0.72	0.00	0.00
time (sec)	N/A	0.170	10.015	0.000	0.000	0.000	6.892	0.000	0.000


Problem 1006	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	61	61	59	0	0	0	44	0	0
N.S.	1	1.00	0.97	0.00	0.00	0.00	0.72	0.00	0.00
time (sec)	N/A	0.166	10.018	0.000	0.000	0.000	3.670	0.000	0.000


Problem 1007	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	61	61	59	0	0	0	44	0	0
N.S.	1	1.00	0.97	0.00	0.00	0.00	0.72	0.00	0.00
time (sec)	N/A	0.166	10.019	0.000	0.000	0.000	4.024	0.000	0.000


Problem 1008	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	59	59	57	0	0	0	44	0	0
N.S.	1	1.00	0.97	0.00	0.00	0.00	0.75	0.00	0.00
time (sec)	N/A	0.164	10.020	0.000	0.000	0.000	7.471	0.000	0.000


Problem 1009	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	59	59	57	0	0	0	48	0	0
N.S.	1	1.00	0.97	0.00	0.00	0.00	0.81	0.00	0.00
time (sec)	N/A	0.164	10.016	0.000	0.000	0.000	13.632	0.000	0.000


Problem 1010	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	345	440	105	0	0	0	29	0	0
N.S.	1	1.28	0.30	0.00	0.00	0.00	0.08	0.00	0.00
time (sec)	N/A	0.337	7.625	0.000	0.000	0.000	0.609	0.000	0.000


Problem 1011	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	321	410	93	0	0	0	29	0	0
N.S.	1	1.28	0.29	0.00	0.00	0.00	0.09	0.00	0.00
time (sec)	N/A	0.297	7.487	0.000	0.000	0.000	0.571	0.000	0.000


Problem 1012	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	297	380	62	0	0	0	29	0	0
N.S.	1	1.28	0.21	0.00	0.00	0.00	0.10	0.00	0.00
time (sec)	N/A	0.282	7.301	0.000	0.000	0.000	0.543	0.000	0.000


Problem 1013	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	B
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	273	353	46	0	0	0	26	0	37
N.S.	1	1.29	0.17	0.00	0.00	0.00	0.10	0.00	0.14
time (sec)	N/A	0.254	7.186	0.000	0.000	0.000	0.521	0.000	4.611


Problem 1014	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	B
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	266	346	49	0	0	0	29	0	40
N.S.	1	1.30	0.18	0.00	0.00	0.00	0.11	0.00	0.15
time (sec)	N/A	0.259	7.226	0.000	0.000	0.000	0.544	0.000	4.763


Problem 1015	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	297	377	51	0	0	0	34	0	0
N.S.	1	1.27	0.17	0.00	0.00	0.00	0.11	0.00	0.00
time (sec)	N/A	0.283	10.010	0.000	0.000	0.000	0.651	0.000	0.000


Problem 1016	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	323	407	51	0	0	0	34	0	0
N.S.	1	1.26	0.16	0.00	0.00	0.00	0.11	0.00	0.00
time (sec)	N/A	0.309	10.014	0.000	0.000	0.000	0.704	0.000	0.000


Problem 1017	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	347	437	51	0	0	0	34	0	0
N.S.	1	1.26	0.15	0.00	0.00	0.00	0.10	0.00	0.00
time (sec)	N/A	0.322	10.022	0.000	0.000	0.000	0.766	0.000	0.000


Problem 1018	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	659	787	90	0	0	0	27	0	0
N.S.	1	1.19	0.14	0.00	0.00	0.00	0.04	0.00	0.00
time (sec)	N/A	0.519	8.170	0.000	0.000	0.000	0.581	0.000	0.000


Problem 1019	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	635	757	79	0	0	0	27	0	0
N.S.	1	1.19	0.12	0.00	0.00	0.00	0.04	0.00	0.00
time (sec)	N/A	0.450	7.794	0.000	0.000	0.000	0.546	0.000	0.000


Problem 1020	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	611	727	62	0	0	0	27	0	0
N.S.	1	1.19	0.10	0.00	0.00	0.00	0.04	0.00	0.00
time (sec)	N/A	0.418	6.978	0.000	0.000	0.000	0.491	0.000	0.000


Problem 1021	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	B
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	577	699	46	0	0	0	24	0	37
N.S.	1	1.21	0.08	0.00	0.00	0.00	0.04	0.00	0.06
time (sec)	N/A	0.408	6.942	0.000	0.000	0.000	0.474	0.000	4.454


Problem 1022	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	B
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	586	727	49	0	0	0	27	0	40
N.S.	1	1.24	0.08	0.00	0.00	0.00	0.05	0.00	0.07
time (sec)	N/A	0.424	7.054	0.000	0.000	0.000	0.530	0.000	4.657


Problem 1023	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	633	757	51	0	0	0	32	0	0
N.S.	1	1.20	0.08	0.00	0.00	0.00	0.05	0.00	0.00
time (sec)	N/A	0.453	10.011	0.000	0.000	0.000	0.637	0.000	0.000


Problem 1024	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	661	787	51	0	0	0	32	0	0
N.S.	1	1.19	0.08	0.00	0.00	0.00	0.05	0.00	0.00
time (sec)	N/A	0.483	10.012	0.000	0.000	0.000	0.672	0.000	0.000


Problem 1025	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	324	416	89	0	0	0	27	0	0
N.S.	1	1.28	0.27	0.00	0.00	0.00	0.08	0.00	0.00
time (sec)	N/A	0.295	8.143	0.000	0.000	0.000	0.520	0.000	0.000


Problem 1026	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	300	386	79	0	0	0	27	0	0
N.S.	1	1.29	0.26	0.00	0.00	0.00	0.09	0.00	0.00
time (sec)	N/A	0.287	8.099	0.000	0.000	0.000	0.516	0.000	0.000


Problem 1027	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	276	356	62	0	0	0	27	0	0
N.S.	1	1.29	0.22	0.00	0.00	0.00	0.10	0.00	0.00
time (sec)	N/A	0.256	7.252	0.000	0.000	0.000	0.503	0.000	0.000


Problem 1028	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	B
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	252	332	46	0	0	0	24	0	37
N.S.	1	1.32	0.18	0.00	0.00	0.00	0.10	0.00	0.15
time (sec)	N/A	0.259	7.038	0.000	0.000	0.000	0.484	0.000	4.517


Problem 1029	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	B
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	273	353	49	0	0	0	27	0	40
N.S.	1	1.29	0.18	0.00	0.00	0.00	0.10	0.00	0.15
time (sec)	N/A	0.262	7.835	0.000	0.000	0.000	0.588	0.000	4.586


Problem 1030	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	300	383	51	0	0	0	32	0	0
N.S.	1	1.28	0.17	0.00	0.00	0.00	0.11	0.00	0.00
time (sec)	N/A	0.295	10.019	0.000	0.000	0.000	0.653	0.000	0.000


Problem 1031	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	326	413	51	0	0	0	32	0	0
N.S.	1	1.27	0.16	0.00	0.00	0.00	0.10	0.00	0.00
time (sec)	N/A	0.310	10.014	0.000	0.000	0.000	0.745	0.000	0.000


Problem 1032	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	654	782	79	0	0	0	27	0	0
N.S.	1	1.20	0.12	0.00	0.00	0.00	0.04	0.00	0.00
time (sec)	N/A	0.488	8.122	0.000	0.000	0.000	0.545	0.000	0.000


Problem 1033	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	630	752	65	0	0	0	27	0	0
N.S.	1	1.19	0.10	0.00	0.00	0.00	0.04	0.00	0.00
time (sec)	N/A	0.457	7.985	0.000	0.000	0.000	0.552	0.000	0.000


Problem 1034	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	583	722	58	0	0	0	27	0	0
N.S.	1	1.24	0.10	0.00	0.00	0.00	0.05	0.00	0.00
time (sec)	N/A	0.443	7.491	0.000	0.000	0.000	0.544	0.000	0.000


Problem 1035	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	B
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	555	681	49	0	0	0	24	0	37
N.S.	1	1.23	0.09	0.00	0.00	0.00	0.04	0.00	0.07
time (sec)	N/A	0.389	7.363	0.000	0.000	0.000	0.536	0.000	4.500


Problem 1036	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	B
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	614	752	52	0	0	0	27	0	40
N.S.	1	1.22	0.08	0.00	0.00	0.00	0.04	0.00	0.07
time (sec)	N/A	0.452	7.832	0.000	0.000	0.000	0.684	0.000	4.668


Problem 1037	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	652	782	54	0	0	0	32	0	0
N.S.	1	1.20	0.08	0.00	0.00	0.00	0.05	0.00	0.00
time (sec)	N/A	0.488	10.051	0.000	0.000	0.000	0.755	0.000	0.000


Problem 1038	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	F	F	F	A	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	680	812	54	0	0	0	32	0	0
N.S.	1	1.19	0.08	0.00	0.00	0.00	0.05	0.00	0.00
time (sec)	N/A	0.519	10.016	0.000	0.000	0.000	0.841	0.000	0.000


Problem 1039	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	A	A	A	B	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD
size	100	95	95	132	106	148	1923	260	183
N.S.	1	0.95	0.95	1.32	1.06	1.48	19.23	2.60	1.83
time (sec)	N/A	0.229	0.105	2.280	0.232	0.247	2.963	0.276	4.608


Problem 1040	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD
size	72	70	64	80	73	98	920	132	117
N.S.	1	0.97	0.89	1.11	1.01	1.36	12.78	1.83	1.62
time (sec)	N/A	0.205	0.055	2.237	0.210	0.254	1.403	0.269	4.602


Problem 1041	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD
size	48	47	40	42	47	58	333	51	68
N.S.	1	0.98	0.83	0.88	0.98	1.21	6.94	1.06	1.42
time (sec)	N/A	0.185	0.045	2.238	0.216	0.257	0.560	0.277	4.584


Problem 1042	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD
size	23	23	22	22	21	25	87	21	21
N.S.	1	1.00	0.96	0.96	0.91	1.09	3.78	0.91	0.91
time (sec)	N/A	0.143	0.003	2.220	0.209	0.260	0.304	0.271	4.516


Problem 1043	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	41	41	41	0	0	0	39	0	0
N.S.	1	1.00	1.00	0.00	0.00	0.00	0.95	0.00	0.00
time (sec)	N/A	0.165	0.040	0.000	0.000	0.000	1.081	0.000	0.000


Problem 1044	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	42	42	42	0	0	0	41	0	0
N.S.	1	1.00	1.00	0.00	0.00	0.00	0.98	0.00	0.00
time (sec)	N/A	0.169	0.033	0.000	0.000	0.000	2.253	0.000	0.000


Problem 1045	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	40	49	49	0	0	0	26	0	0
N.S.	1	1.22	1.22	0.00	0.00	0.00	0.65	0.00	0.00
time (sec)	N/A	0.161	0.046	0.000	0.000	0.000	5.938	0.000	0.000


Problem 1046	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	40	49	49	0	0	0	26	0	0
N.S.	1	1.22	1.22	0.00	0.00	0.00	0.65	0.00	0.00
time (sec)	N/A	0.160	0.039	0.000	0.000	0.000	3.343	0.000	0.000


Problem 1047	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	40	49	49	0	0	0	26	0	0
N.S.	1	1.22	1.22	0.00	0.00	0.00	0.65	0.00	0.00
time (sec)	N/A	0.157	0.031	0.000	0.000	0.000	1.902	0.000	0.000


Problem 1048	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	B
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	35	44	44	0	0	0	22	0	41
N.S.	1	1.26	1.26	0.00	0.00	0.00	0.63	0.00	1.17
time (sec)	N/A	0.157	0.028	0.000	0.000	0.000	1.147	0.000	4.984


Problem 1049	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	B
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	38	47	47	0	0	0	26	0	58
N.S.	1	1.24	1.24	0.00	0.00	0.00	0.68	0.00	1.53
time (sec)	N/A	0.159	0.041	0.000	0.000	0.000	1.789	0.000	4.614


Problem 1050	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	F(-1)	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	42	51	51	0	0	0	0	0	0
N.S.	1	1.21	1.21	0.00	0.00	0.00	0.00	0.00	0.00
time (sec)	N/A	0.159	0.103	0.000	0.000	0.000	0.000	0.000	0.000


Problem 1051	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	F(-1)	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	42	51	51	0	0	0	0	0	0
N.S.	1	1.21	1.21	0.00	0.00	0.00	0.00	0.00	0.00
time (sec)	N/A	0.162	0.131	0.000	0.000	0.000	0.000	0.000	0.000


Problem 1052	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	F(-1)	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	42	51	51	0	0	0	0	0	0
N.S.	1	1.21	1.21	0.00	0.00	0.00	0.00	0.00	0.00
time (sec)	N/A	0.163	0.119	0.000	0.000	0.000	0.000	0.000	0.000


Problem 1053	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	42	51	51	0	0	0	37	0	0
N.S.	1	1.21	1.21	0.00	0.00	0.00	0.88	0.00	0.00
time (sec)	N/A	0.160	0.093	0.000	0.000	0.000	31.976	0.000	0.000


Problem 1054	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	40	49	49	0	0	0	37	0	0
N.S.	1	1.22	1.22	0.00	0.00	0.00	0.92	0.00	0.00
time (sec)	N/A	0.160	0.124	0.000	0.000	0.000	17.371	0.000	0.000


Problem 1055	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	40	49	49	0	0	0	41	0	0
N.S.	1	1.22	1.22	0.00	0.00	0.00	1.02	0.00	0.00
time (sec)	N/A	0.165	0.151	0.000	0.000	0.000	130.710	0.000	0.000


Problem 1056	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	F(-1)	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	42	51	51	0	0	0	0	0	0
N.S.	1	1.21	1.21	0.00	0.00	0.00	0.00	0.00	0.00
time (sec)	N/A	0.157	0.149	0.000	0.000	0.000	0.000	0.000	0.000


Problem 1057	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	F(-1)	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	42	51	51	0	0	0	0	0	0
N.S.	1	1.21	1.21	0.00	0.00	0.00	0.00	0.00	0.00
time (sec)	N/A	0.158	0.143	0.000	0.000	0.000	0.000	0.000	0.000


Problem 1058	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	53	61	63	0	0	0	51	0	0
N.S.	1	1.15	1.19	0.00	0.00	0.00	0.96	0.00	0.00
time (sec)	N/A	0.172	0.057	0.000	0.000	0.000	11.116	0.000	0.000


Problem 1059	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	66	66	64	0	0	0	54	0	0
N.S.	1	1.00	0.97	0.00	0.00	0.00	0.82	0.00	0.00
time (sec)	N/A	0.176	0.014	0.000	0.000	0.000	10.893	0.000	0.000


Problem 1060	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	53	70	66	0	0	0	54	0	0
N.S.	1	1.32	1.25	0.00	0.00	0.00	1.02	0.00	0.00
time (sec)	N/A	0.185	0.038	0.000	0.000	0.000	9.979	0.000	0.000


Problem 1061	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	A	A	A	B	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD
size	105	109	62	81	84	106	452	0	154
N.S.	1	1.04	0.59	0.77	0.80	1.01	4.30	0.00	1.47
time (sec)	N/A	0.234	0.033	2.495	0.218	0.253	9.894	0.000	4.623


Problem 1062	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	53	70	66	0	0	0	54	0	0
N.S.	1	1.32	1.25	0.00	0.00	0.00	1.02	0.00	0.00
time (sec)	N/A	0.193	0.038	0.000	0.000	0.000	9.777	0.000	0.000


Problem 1063	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	C	A	A	A	B	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD
size	67	67	62	45	59	67	162	0	96
N.S.	1	1.00	0.93	0.67	0.88	1.00	2.42	0.00	1.43
time (sec)	N/A	0.180	0.032	2.500	0.224	0.256	9.766	0.000	4.551


Problem 1064	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	53	70	66	0	0	0	54	0	0
N.S.	1	1.32	1.25	0.00	0.00	0.00	1.02	0.00	0.00
time (sec)	N/A	0.189	0.036	0.000	0.000	0.000	10.087	0.000	0.000


Problem 1065	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	A	A	A	A	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD
size	30	30	29	29	37	34	36	0	52
N.S.	1	1.00	0.97	0.97	1.23	1.13	1.20	0.00	1.73
time (sec)	N/A	0.152	0.030	2.505	0.216	0.258	9.832	0.000	4.529


Problem 1066	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	53	70	66	0	0	0	51	0	0
N.S.	1	1.32	1.25	0.00	0.00	0.00	0.96	0.00	0.00
time (sec)	N/A	0.192	0.037	0.000	0.000	0.000	9.783	0.000	0.000


Problem 1067	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	43	56	56	0	0	0	37	0	0
N.S.	1	1.30	1.30	0.00	0.00	0.00	0.86	0.00	0.00
time (sec)	N/A	0.178	0.025	0.000	0.000	0.000	6.141	0.000	0.000


Problem 1068	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	52	69	65	0	0	0	32	0	0
N.S.	1	1.33	1.25	0.00	0.00	0.00	0.62	0.00	0.00
time (sec)	N/A	0.185	0.033	0.000	0.000	0.000	7.972	0.000	0.000


Problem 1069	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	49	64	61	0	0	0	39	0	0
N.S.	1	1.31	1.24	0.00	0.00	0.00	0.80	0.00	0.00
time (sec)	N/A	0.180	0.030	0.000	0.000	0.000	10.036	0.000	0.000


Problem 1070	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	52	69	65	0	0	0	46	0	0
N.S.	1	1.33	1.25	0.00	0.00	0.00	0.88	0.00	0.00
time (sec)	N/A	0.183	0.032	0.000	0.000	0.000	10.254	0.000	0.000


Problem 1071	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	N/A	A	A	F	F	F	C	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD
size	49	64	61	0	0	0	39	0	0
N.S.	1	1.31	1.24	0.00	0.00	0.00	0.80	0.00	0.00
time (sec)	N/A	0.181	0.032	0.000	0.000	0.000	11.406	0.000	0.000

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