Integrals 1801 to 1900

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2.2.19 Integrals 1801 to 1900

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 1801	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	B	F(-1)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	32	32	32	27	0	104	0	0	46	199
N.S.	1	1.00	1.00	0.84	0.00	3.25	0.00	0.00	1.44	6.22
time (sec)	N/A	0.141	0.028	0.372	0.000	0.230	0.000	0.000	0.000	0.704


Problem 1802	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	B	F(-1)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	66	66	46	54	0	235	0	0	57	189
N.S.	1	1.00	0.70	0.82	0.00	3.56	0.00	0.00	0.86	2.86
time (sec)	N/A	0.166	0.249	0.768	0.000	0.227	0.000	0.000	0.000	0.897


Problem 1803	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	B	F(-1)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	101	114	77	105	0	427	0	0	68	278
N.S.	1	1.13	0.76	1.04	0.00	4.23	0.00	0.00	0.67	2.75
time (sec)	N/A	0.193	0.400	0.922	0.000	0.243	0.000	0.000	0.000	1.344


Problem 1804	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	B	F(-1)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	136	162	118	171	0	649	0	0	79	385
N.S.	1	1.19	0.87	1.26	0.00	4.77	0.00	0.00	0.58	2.83
time (sec)	N/A	0.211	1.080	1.417	0.000	0.263	0.000	0.000	0.000	1.363


Problem 1805	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	B	F	F	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	424	443	317	0	0	2585	0	0	40	0
N.S.	1	1.04	0.75	0.00	0.00	6.10	0.00	0.00	0.09	0.00
time (sec)	N/A	0.516	0.731	0.000	0.000	0.290	0.000	0.000	5.182	0.000


Problem 1806	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	B	F	F	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	378	402	293	0	0	1443	0	0	17	0
N.S.	1	1.06	0.78	0.00	0.00	3.82	0.00	0.00	0.04	0.00
time (sec)	N/A	0.460	0.808	0.000	0.000	0.265	0.000	0.000	1.673	0.000


Problem 1807	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	A	F	F	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	309	369	222	0	0	402	0	0	17	0
N.S.	1	1.19	0.72	0.00	0.00	1.30	0.00	0.00	0.06	0.00
time (sec)	N/A	0.424	0.462	0.000	0.000	0.236	0.000	0.000	0.000	0.000


Problem 1808	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	A	F	F	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	32	32	32	27	0	42	0	0	161	27
N.S.	1	1.00	1.00	0.84	0.00	1.31	0.00	0.00	5.03	0.84
time (sec)	N/A	0.141	0.026	0.392	0.000	0.225	0.000	0.000	4.047	0.705


Problem 1809	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	B	F(-1)	F	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	66	66	46	54	0	118	0	0	541	127
N.S.	1	1.00	0.70	0.82	0.00	1.79	0.00	0.00	8.20	1.92
time (sec)	N/A	0.162	0.200	0.766	0.000	0.230	0.000	0.000	15.208	1.050


Problem 1810	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	B	F(-1)	F	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	101	114	77	105	0	252	0	0	894	203
N.S.	1	1.13	0.76	1.04	0.00	2.50	0.00	0.00	8.85	2.01
time (sec)	N/A	0.190	0.293	0.922	0.000	0.241	0.000	0.000	24.651	0.981


Problem 1811	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	B	F(-1)	F	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	136	162	118	171	0	420	0	0	1330	292
N.S.	1	1.19	0.87	1.26	0.00	3.09	0.00	0.00	9.78	2.15
time (sec)	N/A	0.214	0.952	0.925	0.000	0.260	0.000	0.000	38.350	1.380


Problem 1812	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F(-1)	F(-1)	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	82	82	73	0	0	0	0	0	40	0
N.S.	1	1.00	0.89	0.00	0.00	0.00	0.00	0.00	0.49	0.00
time (sec)	N/A	0.179	0.042	0.000	0.000	0.000	0.000	0.000	7.353	0.000


Problem 1813	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	74	74	73	0	0	0	0	0	17	0
N.S.	1	1.00	0.99	0.00	0.00	0.00	0.00	0.00	0.23	0.00
time (sec)	N/A	0.172	0.020	0.000	0.000	0.000	0.000	0.000	1.835	0.000


Problem 1814	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	74	74	73	0	0	0	0	0	17	0
N.S.	1	1.00	0.99	0.00	0.00	0.00	0.00	0.00	0.23	0.00
time (sec)	N/A	0.171	0.020	0.000	0.000	0.000	0.000	0.000	0.761	0.000


Problem 1815	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	81	81	73	0	0	0	0	0	38	0
N.S.	1	1.00	0.90	0.00	0.00	0.00	0.00	0.00	0.47	0.00
time (sec)	N/A	0.175	0.028	0.000	0.000	0.000	0.000	0.000	2.184	0.000


Problem 1816	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	B	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	82	82	73	0	0	0	0	0	176	0
N.S.	1	1.00	0.89	0.00	0.00	0.00	0.00	0.00	2.15	0.00
time (sec)	N/A	0.176	0.037	0.000	0.000	0.000	0.000	0.000	13.162	0.000


Problem 1817	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F(-1)	F	B	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	84	84	81	0	0	0	0	0	375	0
N.S.	1	1.00	0.96	0.00	0.00	0.00	0.00	0.00	4.46	0.00
time (sec)	N/A	0.181	0.030	0.000	0.000	0.000	0.000	0.000	22.033	0.000


Problem 1818	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F(-1)	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	82	82	71	0	0	0	0	0	68	0
N.S.	1	1.00	0.87	0.00	0.00	0.00	0.00	0.00	0.83	0.00
time (sec)	N/A	0.177	0.045	0.000	0.000	0.000	0.000	0.000	10.226	0.000


Problem 1819	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	80	80	71	0	0	0	0	0	40	0
N.S.	1	1.00	0.89	0.00	0.00	0.00	0.00	0.00	0.50	0.00
time (sec)	N/A	0.174	0.031	0.000	0.000	0.000	0.000	0.000	5.013	0.000


Problem 1820	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	72	72	71	0	0	0	0	0	17	0
N.S.	1	1.00	0.99	0.00	0.00	0.00	0.00	0.00	0.24	0.00
time (sec)	N/A	0.173	0.021	0.000	0.000	0.000	0.000	0.000	1.686	0.000


Problem 1821	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	B	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	72	72	71	0	0	0	0	0	87	0
N.S.	1	1.00	0.99	0.00	0.00	0.00	0.00	0.00	1.21	0.00
time (sec)	N/A	0.175	0.019	0.000	0.000	0.000	0.000	0.000	0.357	0.000


Problem 1822	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	79	79	71	0	0	0	0	0	133	0
N.S.	1	1.00	0.90	0.00	0.00	0.00	0.00	0.00	1.68	0.00
time (sec)	N/A	0.169	0.026	0.000	0.000	0.000	0.000	0.000	2.419	0.000


Problem 1823	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F(-1)	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	80	80	79	0	0	0	0	0	181	0
N.S.	1	1.00	0.99	0.00	0.00	0.00	0.00	0.00	2.26	0.00
time (sec)	N/A	0.169	0.020	0.000	0.000	0.000	0.000	0.000	13.542	0.000


Problem 1824	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	B	F(-1)	F	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	424	434	317	0	0	2575	0	0	17	0
N.S.	1	1.02	0.75	0.00	0.00	6.07	0.00	0.00	0.04	0.00
time (sec)	N/A	0.482	0.759	0.000	0.000	0.293	0.000	0.000	0.000	0.000


Problem 1825	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	B	F	F	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	378	393	295	0	0	1455	0	0	17	0
N.S.	1	1.04	0.78	0.00	0.00	3.85	0.00	0.00	0.04	0.00
time (sec)	N/A	0.455	0.804	0.000	0.000	0.258	0.000	0.000	0.000	0.000


Problem 1826	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	A	F	F	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	309	362	223	0	0	402	0	0	17	0
N.S.	1	1.17	0.72	0.00	0.00	1.30	0.00	0.00	0.06	0.00
time (sec)	N/A	0.419	0.450	0.000	0.000	0.231	0.000	0.000	0.000	0.000


Problem 1827	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	A	F	F	B	F(-1)
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	30	30	30	27	0	42	0	0	87	0
N.S.	1	1.00	1.00	0.90	0.00	1.40	0.00	0.00	2.90	0.00
time (sec)	N/A	0.142	0.022	0.401	0.000	0.219	0.000	0.000	2.670	0.000


Problem 1828	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	B	F	F	B	F(-1)
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	66	66	46	53	0	118	0	0	340	0
N.S.	1	1.00	0.70	0.80	0.00	1.79	0.00	0.00	5.15	0.00
time (sec)	N/A	0.165	0.169	0.796	0.000	0.225	0.000	0.000	8.069	0.000


Problem 1829	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	B	F(-1)	F	B	F(-1)
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	101	114	77	105	0	252	0	0	638	0
N.S.	1	1.13	0.76	1.04	0.00	2.50	0.00	0.00	6.32	0.00
time (sec)	N/A	0.187	0.304	0.943	0.000	0.224	0.000	0.000	14.778	0.000


Problem 1830	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	B	F(-1)	F	B	F(-1)
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	136	162	118	171	0	420	0	0	985	0
N.S.	1	1.19	0.87	1.26	0.00	3.09	0.00	0.00	7.24	0.00
time (sec)	N/A	0.208	0.904	0.942	0.000	0.239	0.000	0.000	26.822	0.000


Problem 1831	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	B	F(-1)	F	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	449	473	357	0	0	2686	0	0	825	0
N.S.	1	1.05	0.80	0.00	0.00	5.98	0.00	0.00	1.84	0.00
time (sec)	N/A	0.533	1.046	0.000	0.000	0.282	0.000	0.000	12.434	0.000


Problem 1832	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	B	F	F	F	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	403	432	318	0	0	1562	0	0	531	0
N.S.	1	1.07	0.79	0.00	0.00	3.88	0.00	0.00	1.32	0.00
time (sec)	N/A	0.504	0.945	0.000	0.000	0.279	0.000	0.000	9.087	0.000


Problem 1833	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	B	F	F	B	F(-1)
veriﬁed	N/A	No	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	332	397	268	0	0	504	0	0	255	0
N.S.	1	1.20	0.81	0.00	0.00	1.52	0.00	0.00	0.77	0.00
time (sec)	N/A	0.472	0.533	0.000	0.000	0.243	0.000	0.000	3.105	0.000


Problem 1834	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	A	F	F	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	30	30	30	27	0	42	0	0	87	26
N.S.	1	1.00	1.00	0.90	0.00	1.40	0.00	0.00	2.90	0.87
time (sec)	N/A	0.148	0.025	0.377	0.000	0.225	0.000	0.000	3.205	0.756


Problem 1835	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	B	F	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	64	64	45	53	0	126	0	0	133	72
N.S.	1	1.00	0.70	0.83	0.00	1.97	0.00	0.00	2.08	1.12
time (sec)	N/A	0.172	0.283	0.791	0.000	0.233	0.000	0.000	9.514	0.976


Problem 1836	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	B	F(-1)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	98	110	77	105	0	273	0	0	181	132
N.S.	1	1.12	0.79	1.07	0.00	2.79	0.00	0.00	1.85	1.35
time (sec)	N/A	0.198	0.371	0.955	0.000	0.236	0.000	0.000	18.610	1.219


Problem 1837	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	B	F(-1)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	134	158	118	171	0	457	0	0	229	209
N.S.	1	1.18	0.88	1.28	0.00	3.41	0.00	0.00	1.71	1.56
time (sec)	N/A	0.219	0.945	0.952	0.000	0.257	0.000	0.000	29.723	1.449


Problem 1838	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F(-1)	F(-1)	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	80	80	71	0	0	0	0	0	318	0
N.S.	1	1.00	0.89	0.00	0.00	0.00	0.00	0.00	3.98	0.00
time (sec)	N/A	0.185	0.039	0.000	0.000	0.000	0.000	0.000	18.495	0.000


Problem 1839	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	72	72	71	0	0	0	0	0	270	0
N.S.	1	1.00	0.99	0.00	0.00	0.00	0.00	0.00	3.75	0.00
time (sec)	N/A	0.172	0.019	0.000	0.000	0.000	0.000	0.000	29.145	0.000


Problem 1840	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	72	72	71	0	0	0	0	0	38	0
N.S.	1	1.00	0.99	0.00	0.00	0.00	0.00	0.00	0.53	0.00
time (sec)	N/A	0.173	0.021	0.000	0.000	0.000	0.000	0.000	1.756	0.000


Problem 1841	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	B	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	79	79	71	0	0	0	0	0	87	0
N.S.	1	1.00	0.90	0.00	0.00	0.00	0.00	0.00	1.10	0.00
time (sec)	N/A	0.177	0.029	0.000	0.000	0.000	0.000	0.000	3.951	0.000


Problem 1842	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F(-1)	F	B	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	80	80	71	0	0	0	0	0	216	0
N.S.	1	1.00	0.89	0.00	0.00	0.00	0.00	0.00	2.70	0.00
time (sec)	N/A	0.182	0.037	0.000	0.000	0.000	0.000	0.000	10.105	0.000


Problem 1843	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F(-1)	F	B	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	82	82	79	0	0	0	0	0	420	0
N.S.	1	1.00	0.96	0.00	0.00	0.00	0.00	0.00	5.12	0.00
time (sec)	N/A	0.184	0.027	0.000	0.000	0.000	0.000	0.000	16.281	0.000


Problem 1844	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	B	A	B	B	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	11	11	11	12	106	17	20	23	14	11
N.S.	1	1.00	1.00	1.09	9.64	1.55	1.82	2.09	1.27	1.00
time (sec)	N/A	0.134	0.045	0.373	0.214	0.224	0.106	0.281	0.002	0.535


Problem 1845	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F(-2)	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	61	74	73	0	0	0	0	0	0	0
N.S.	1	1.21	1.20	0.00	0.00	0.00	0.00	0.00	0.00	0.00
time (sec)	N/A	0.190	0.042	0.000	0.000	0.000	0.000	0.000	0.198	0.000


Problem 1846	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	B	B	B	B	B	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	110	110	94	389	246	497	4058	833	546	478
N.S.	1	1.00	0.85	3.54	2.24	4.52	36.89	7.57	4.96	4.35
time (sec)	N/A	0.256	0.090	0.406	0.215	0.229	1.133	0.309	0.016	0.985


Problem 1847	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	B	A	B	B	B	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	78	78	67	159	138	235	1506	385	241	226
N.S.	1	1.00	0.86	2.04	1.77	3.01	19.31	4.94	3.09	2.90
time (sec)	N/A	0.217	0.083	0.394	0.216	0.225	0.599	0.297	0.008	0.794


Problem 1848	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	A	A	B	B	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	46	46	41	49	63	83	377	132	75	88
N.S.	1	1.00	0.89	1.07	1.37	1.80	8.20	2.87	1.63	1.91
time (sec)	N/A	0.182	0.045	0.381	0.200	0.235	0.342	0.285	0.003	0.456


Problem 1849	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	51	51	51	0	0	0	0	0	94	0
N.S.	1	1.00	1.00	0.00	0.00	0.00	0.00	0.00	1.84	0.00
time (sec)	N/A	0.166	0.041	0.000	0.000	0.000	0.000	0.000	0.034	0.000


Problem 1850	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	52	52	52	0	0	0	0	0	1219	0
N.S.	1	1.00	1.00	0.00	0.00	0.00	0.00	0.00	23.44	0.00
time (sec)	N/A	0.163	0.042	0.000	0.000	0.000	0.000	0.000	0.103	0.000


Problem 1851	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	54	54	54	0	0	0	0	0	0	0
N.S.	1	1.00	1.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
time (sec)	N/A	0.166	0.044	0.000	0.000	0.000	0.000	0.000	0.165	0.000


Problem 1852	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	B	B	B	B	B	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	111	111	95	386	246	496	4058	833	546	478
N.S.	1	1.00	0.86	3.48	2.22	4.47	36.56	7.50	4.92	4.31
time (sec)	N/A	0.255	0.084	0.412	0.243	0.238	1.021	0.284	0.016	0.998


Problem 1853	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	B	A	B	B	B	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	78	78	67	159	138	237	1506	385	241	226
N.S.	1	1.00	0.86	2.04	1.77	3.04	19.31	4.94	3.09	2.90
time (sec)	N/A	0.218	0.081	0.400	0.236	0.227	0.578	0.307	0.008	0.578


Problem 1854	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	A	A	B	B	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	47	47	41	46	63	83	377	132	75	88
N.S.	1	1.00	0.87	0.98	1.34	1.77	8.02	2.81	1.60	1.87
time (sec)	N/A	0.182	0.044	0.382	0.231	0.228	0.343	0.277	0.003	0.453


Problem 1855	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	A	A	A	A	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	18	18	18	19	18	20	20	18	21	18
N.S.	1	1.00	1.00	1.06	1.00	1.11	1.11	1.00	1.17	1.00
time (sec)	N/A	0.137	0.002	0.372	0.212	0.225	0.019	0.299	0.001	0.451


Problem 1856	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	51	51	51	0	0	0	0	0	94	0
N.S.	1	1.00	1.00	0.00	0.00	0.00	0.00	0.00	1.84	0.00
time (sec)	N/A	0.163	0.040	0.000	0.000	0.000	0.000	0.000	0.035	0.000


Problem 1857	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	51	51	52	0	0	0	0	0	1218	0
N.S.	1	1.00	1.02	0.00	0.00	0.00	0.00	0.00	23.88	0.00
time (sec)	N/A	0.163	0.041	0.000	0.000	0.000	0.000	0.000	0.104	0.000


Problem 1858	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	54	54	54	0	0	0	0	0	0	0
N.S.	1	1.00	1.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
time (sec)	N/A	0.165	0.043	0.000	0.000	0.000	0.000	0.000	0.163	0.000


Problem 1859	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	B	F	B	F(-2)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	143	146	112	322	0	512	0	0	86	528
N.S.	1	1.02	0.78	2.25	0.00	3.58	0.00	0.00	0.60	3.69
time (sec)	N/A	0.237	0.077	0.540	0.000	0.240	0.000	0.000	0.017	1.223


Problem 1860	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	B	F(-2)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	86	86	59	127	0	206	0	0	68	220
N.S.	1	1.00	0.69	1.48	0.00	2.40	0.00	0.00	0.79	2.56
time (sec)	N/A	0.187	0.056	0.497	0.000	0.237	0.000	0.000	0.014	0.706


Problem 1861	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	A	F(-2)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	39	39	36	45	0	60	0	0	50	102
N.S.	1	1.00	0.92	1.15	0.00	1.54	0.00	0.00	1.28	2.62
time (sec)	N/A	0.150	0.040	0.492	0.000	0.232	0.000	0.000	0.010	0.534


Problem 1862	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	66	66	65	0	0	0	0	0	32	0
N.S.	1	1.00	0.98	0.00	0.00	0.00	0.00	0.00	0.48	0.00
time (sec)	N/A	0.181	0.048	0.000	0.000	0.000	0.000	0.000	0.007	0.000


Problem 1863	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F(-2)	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	72	72	71	0	0	0	0	0	19	0
N.S.	1	1.00	0.99	0.00	0.00	0.00	0.00	0.00	0.26	0.00
time (sec)	N/A	0.182	0.037	0.000	0.000	0.000	0.000	0.000	0.006	0.000


Problem 1864	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F(-2)	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	72	72	89	0	0	0	0	0	44	0
N.S.	1	1.00	1.24	0.00	0.00	0.00	0.00	0.00	0.61	0.00
time (sec)	N/A	0.179	0.059	0.000	0.000	0.000	0.000	0.000	0.019	0.000


Problem 1865	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F(-2)	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	72	72	92	0	0	0	0	0	74	0
N.S.	1	1.00	1.28	0.00	0.00	0.00	0.00	0.00	1.03	0.00
time (sec)	N/A	0.177	0.059	0.000	0.000	0.000	0.000	0.000	0.028	0.000


Problem 1866	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F(-2)	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	72	72	71	0	0	0	0	0	19	0
N.S.	1	1.00	0.99	0.00	0.00	0.00	0.00	0.00	0.26	0.00
time (sec)	N/A	0.188	0.038	0.000	0.000	0.000	0.000	0.000	0.008	0.000


Problem 1867	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	75	75	74	0	0	0	0	0	32	0
N.S.	1	1.00	0.99	0.00	0.00	0.00	0.00	0.00	0.43	0.00
time (sec)	N/A	0.185	0.045	0.000	0.000	0.000	0.000	0.000	0.007	0.000


Problem 1868	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	A	F(-2)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	37	37	38	41	0	59	0	0	50	97
N.S.	1	1.00	1.03	1.11	0.00	1.59	0.00	0.00	1.35	2.62
time (sec)	N/A	0.150	0.038	0.529	0.000	0.235	0.000	0.000	0.009	0.583


Problem 1869	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	B	F(-2)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	80	80	60	123	0	207	0	0	68	214
N.S.	1	1.00	0.75	1.54	0.00	2.59	0.00	0.00	0.85	2.68
time (sec)	N/A	0.187	0.050	0.528	0.000	0.235	0.000	0.000	0.012	0.761


Problem 1870	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	B	F	B	F(-2)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	131	136	113	318	0	509	0	0	86	525
N.S.	1	1.04	0.86	2.43	0.00	3.89	0.00	0.00	0.66	4.01
time (sec)	N/A	0.228	0.069	0.591	0.000	0.247	0.000	0.000	0.015	0.910


Problem 1871	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	B	F	B	F(-2)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	186	192	195	661	0	959	0	0	104	944
N.S.	1	1.03	1.05	3.55	0.00	5.16	0.00	0.00	0.56	5.08
time (sec)	N/A	0.266	0.094	1.033	0.000	0.273	0.000	0.000	0.018	1.695


Problem 1872	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F(-2)	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	72	72	71	0	0	0	0	0	19	0
N.S.	1	1.00	0.99	0.00	0.00	0.00	0.00	0.00	0.26	0.00
time (sec)	N/A	0.180	0.001	0.000	0.000	0.000	0.000	0.000	0.006	0.000


Problem 1873	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	75	75	74	0	0	0	0	0	32	0
N.S.	1	1.00	0.99	0.00	0.00	0.00	0.00	0.00	0.43	0.00
time (sec)	N/A	0.188	0.047	0.000	0.000	0.000	0.000	0.000	0.007	0.000


Problem 1874	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	A	F(-2)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	36	36	36	42	0	58	0	0	50	98
N.S.	1	1.00	1.00	1.17	0.00	1.61	0.00	0.00	1.39	2.72
time (sec)	N/A	0.147	0.039	0.524	0.000	0.233	0.000	0.000	0.010	0.565


Problem 1875	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	B	F(-2)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	79	79	59	124	0	205	0	0	68	214
N.S.	1	1.00	0.75	1.57	0.00	2.59	0.00	0.00	0.86	2.71
time (sec)	N/A	0.178	0.052	0.528	0.000	0.237	0.000	0.000	0.012	0.899


Problem 1876	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	B	F	B	F(-2)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	130	134	112	319	0	507	0	0	86	528
N.S.	1	1.03	0.86	2.45	0.00	3.90	0.00	0.00	0.66	4.06
time (sec)	N/A	0.219	0.071	0.586	0.000	0.246	0.000	0.000	0.015	0.978


Problem 1877	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	B	F	B	F(-2)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	185	189	195	662	0	954	0	0	104	945
N.S.	1	1.02	1.05	3.58	0.00	5.16	0.00	0.00	0.56	5.11
time (sec)	N/A	0.249	0.092	0.586	0.000	0.283	0.000	0.000	0.018	1.709


Problem 1878	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	83	83	75	0	0	0	0	0	106	0
N.S.	1	1.00	0.90	0.00	0.00	0.00	0.00	0.00	1.28	0.00
time (sec)	N/A	0.195	0.073	0.000	0.000	0.000	0.000	0.000	0.033	0.000


Problem 1879	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	84	84	83	0	0	0	0	0	70	0
N.S.	1	1.00	0.99	0.00	0.00	0.00	0.00	0.00	0.83	0.00
time (sec)	N/A	0.194	0.060	0.000	0.000	0.000	0.000	0.000	0.021	0.000


Problem 1880	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	51	51	51	0	0	0	0	0	94	0
N.S.	1	1.00	1.00	0.00	0.00	0.00	0.00	0.00	1.84	0.00
time (sec)	N/A	0.159	0.006	0.000	0.000	0.000	0.000	0.000	0.034	0.000


Problem 1881	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	A	A	B	A	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	57	57	53	57	92	93	233	78	115	46
N.S.	1	1.00	0.93	1.00	1.61	1.63	4.09	1.37	2.02	0.81
time (sec)	N/A	0.204	0.017	0.400	0.205	0.225	0.361	0.274	0.008	0.581


Problem 1882	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	A	F	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	95	95	54	57	0	85	0	0	478	81
N.S.	1	1.00	0.57	0.60	0.00	0.89	0.00	0.00	5.03	0.85
time (sec)	N/A	0.205	0.178	1.199	0.000	0.241	0.000	0.000	0.065	1.068


Problem 1883	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	A	F(-1)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	97	97	46	66	0	84	0	0	180	119
N.S.	1	1.00	0.47	0.68	0.00	0.87	0.00	0.00	1.86	1.23
time (sec)	N/A	0.199	0.266	1.268	0.000	0.241	0.000	0.000	0.031	2.400


Problem 1884	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	F	A	F(-1)	F	F	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	97	97	46	66	0	84	0	0	180	142
N.S.	1	1.00	0.47	0.68	0.00	0.87	0.00	0.00	1.86	1.46
time (sec)	N/A	0.197	0.127	0.607	0.000	0.236	0.000	0.000	0.031	0.895


Problem 1885	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	C	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	30	30	30	0	0	0	29	0	97	0
N.S.	1	1.00	1.00	0.00	0.00	0.00	0.97	0.00	3.23	0.00
time (sec)	N/A	0.144	0.062	0.000	0.000	0.000	1.193	0.000	0.026	0.000


Problem 1886	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	C	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	35	35	35	0	0	0	31	0	96	0
N.S.	1	1.00	1.00	0.00	0.00	0.00	0.89	0.00	2.74	0.00
time (sec)	N/A	0.147	0.062	0.000	0.000	0.000	1.160	0.000	0.034	0.000


Problem 1887	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	C	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	33	33	33	0	0	0	37	0	693	0
N.S.	1	1.00	1.00	0.00	0.00	0.00	1.12	0.00	21.00	0.00
time (sec)	N/A	0.146	0.076	0.000	0.000	0.000	46.818	0.000	0.621	0.000


Problem 1888	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	C	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	37	37	37	0	0	0	42	0	693	0
N.S.	1	1.00	1.00	0.00	0.00	0.00	1.14	0.00	18.73	0.00
time (sec)	N/A	0.144	0.076	0.000	0.000	0.000	46.607	0.000	0.614	0.000


Problem 1889	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	C	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	47	47	47	0	0	0	39	0	19	0
N.S.	1	1.00	1.00	0.00	0.00	0.00	0.83	0.00	0.40	0.00
time (sec)	N/A	0.166	0.029	0.000	0.000	0.000	14.527	0.000	0.003	0.000


Problem 1890	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	F	F	F	F(-2)	F	F	F(-1)
veriﬁed	N/A	Yes	Yes	N/A	TBD	TBD	TBD	TBD	TBD	TBD
size	45	45	88	0	0	0	0	0	0	0
N.S.	1	1.00	1.96	0.00	0.00	0.00	0.00	0.00	0.00	0.00
time (sec)	N/A	0.167	0.025	0.000	0.000	0.000	0.000	0.000	0.232	0.000


Problem 1891	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	A	A	A	A	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	28	28	28	23	22	22	22	22	23	22
N.S.	1	1.00	1.00	0.82	0.79	0.79	0.79	0.79	0.82	0.79
time (sec)	N/A	0.151	0.000	0.014	0.193	0.211	0.015	0.283	0.001	0.047


Problem 1892	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	A	A	A	A	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	15	15	15	11	11	11	8	11	10	10
N.S.	1	1.00	1.00	0.73	0.73	0.73	0.53	0.73	0.67	0.67
time (sec)	N/A	0.141	0.000	0.012	0.203	0.212	0.015	0.282	0.000	0.051


Problem 1893	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	A	A	A	A	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	11	11	11	9	9	9	5	9	8	8
N.S.	1	1.00	1.00	0.82	0.82	0.82	0.45	0.82	0.73	0.73
time (sec)	N/A	0.136	0.000	0.012	0.199	0.214	0.014	0.288	0.000	0.024


Problem 1894	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	A	A	A	A	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	9	11	9	10	9	9	7	9	7	7
N.S.	1	1.22	1.00	1.11	1.00	1.00	0.78	1.00	0.78	0.78
time (sec)	N/A	0.127	0.000	0.008	0.253	0.209	0.014	0.288	0.000	0.043


Problem 1895	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	A	A	A	A	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	14	14	14	13	12	12	10	12	12	12
N.S.	1	1.00	1.00	0.93	0.86	0.86	0.71	0.86	0.86	0.86
time (sec)	N/A	0.140	0.000	0.030	0.225	0.213	0.015	0.294	0.000	0.029


Problem 1896	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	A	A	A	A	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	11	11	11	10	9	9	8	9	10	10
N.S.	1	1.00	1.00	0.91	0.82	0.82	0.73	0.82	0.91	0.91
time (sec)	N/A	0.138	0.000	0.011	0.196	0.217	0.015	0.289	0.001	0.028


Problem 1897	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	A	A	A	A	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	15	15	15	9	11	11	8	11	8	8
N.S.	1	1.00	1.00	0.60	0.73	0.73	0.53	0.73	0.53	0.53
time (sec)	N/A	0.141	0.000	0.011	0.193	0.210	0.016	0.279	0.000	0.028


Problem 1898	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	A	A	A	A	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	18	18	18	14	14	14	15	14	13	13
N.S.	1	1.00	1.00	0.78	0.78	0.78	0.83	0.78	0.72	0.72
time (sec)	N/A	0.143	0.000	0.010	0.215	0.218	0.015	0.271	0.000	0.026


Problem 1899	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	A	A	A	A	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	20	20	20	16	16	16	12	16	15	15
N.S.	1	1.00	1.00	0.80	0.80	0.80	0.60	0.80	0.75	0.75
time (sec)	N/A	0.144	0.000	0.012	0.201	0.216	0.015	0.294	0.001	0.028


Problem 1900	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad

grade	N/A	A	A	A	A	A	A	A	B	B
veriﬁed	N/A	Yes	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	16	16	16	13	12	12	10	12	15	12
N.S.	1	1.00	1.00	0.81	0.75	0.75	0.62	0.75	0.94	0.75
time (sec)	N/A	0.143	0.000	0.012	0.201	0.214	0.016	0.284	0.000	0.024

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