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Integrals 101 to 137

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 101

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

130 130 68 112 64 70 56 125 101 100

N.S.

1 1.00 0.52 0.86 0.49 0.54 0.43 0.96 0.78 0.77

time (sec)

N/A 0.643 0.273 0.066 0.127 0.074 1.262 0.113 0.203 22.639

Problem 102

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

198 198 81 167 63 83 53 183 143 142

N.S.

1 1.00 0.41 0.84 0.32 0.42 0.27 0.92 0.72 0.72

time (sec)

N/A 0.814 0.322 0.075 0.128 0.064 1.146 0.108 0.163 22.643

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B A A F F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 86 433 123 161 0 0 359 0

N.S.

1 1.00 0.62 3.12 0.88 1.16 0.00 0.00 2.58 0.00

time (sec)

N/A 0.977 0.344 0.563 0.168 0.074 0.000 0.000 0.193 0.000

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

219 414 159 250 328 228 323 9584 249 249

N.S.

1 1.89 0.73 1.14 1.50 1.04 1.47 43.76 1.14 1.14

time (sec)

N/A 1.635 0.447 0.079 0.067 0.071 0.112 0.225 0.170 22.647

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

170 328 121 197 262 178 260 6582 196 196

N.S.

1 1.93 0.71 1.16 1.54 1.05 1.53 38.72 1.15 1.15

time (sec)

N/A 1.447 0.425 0.066 0.056 0.069 0.102 0.213 0.160 22.517

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

129 242 91 144 196 132 199 4114 143 143

N.S.

1 1.88 0.71 1.12 1.52 1.02 1.54 31.89 1.11 1.11

time (sec)

N/A 1.111 0.356 0.055 0.052 0.072 0.083 0.168 0.178 23.112

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

85 95 58 93 134 85 134 2264 92 92

N.S.

1 1.12 0.68 1.09 1.58 1.00 1.58 26.64 1.08 1.08

time (sec)

N/A 0.591 0.269 0.045 0.050 0.100 0.073 0.152 0.171 22.677

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

96 96 54 118 87 75 0 0 80 80

N.S.

1 1.00 0.56 1.23 0.91 0.78 0.00 0.00 0.83 0.83

time (sec)

N/A 0.787 0.389 0.066 0.118 0.070 0.000 0.000 0.174 22.676

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 58 153 68 83 0 0 86 89

N.S.

1 1.00 0.68 1.80 0.80 0.98 0.00 0.00 1.01 1.05

time (sec)

N/A 0.831 0.420 0.086 0.118 0.071 0.000 0.000 0.187 22.690

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

136 136 76 208 74 89 0 0 108 133

N.S.

1 1.00 0.56 1.53 0.54 0.65 0.00 0.00 0.79 0.98

time (sec)

N/A 1.042 0.389 0.100 0.153 0.068 0.000 0.000 0.176 22.689

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

217 217 116 294 85 137 0 0 173 202

N.S.

1 1.00 0.53 1.35 0.39 0.63 0.00 0.00 0.80 0.93

time (sec)

N/A 1.254 0.444 0.112 0.163 0.068 0.000 0.000 0.193 22.879

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

321 321 156 386 93 186 0 0 244 258

N.S.

1 1.00 0.49 1.20 0.29 0.58 0.00 0.00 0.76 0.80

time (sec)

N/A 1.479 0.521 0.115 0.184 0.073 0.000 0.000 0.165 22.958

Problem 113

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

805 754 458 900 894 544 1445 1096 1064 803

N.S.

1 0.94 0.57 1.12 1.11 0.68 1.80 1.36 1.32 1.00

time (sec)

N/A 2.204 7.242 0.152 0.089 0.074 0.273 0.121 0.173 23.286

Problem 114

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

498 495 320 560 599 354 899 674 642 537

N.S.

1 0.99 0.64 1.12 1.20 0.71 1.81 1.35 1.29 1.08

time (sec)

N/A 1.586 2.666 0.111 0.082 0.074 0.196 0.135 0.171 23.020

Problem 115

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

275 271 191 276 344 197 447 331 300 264

N.S.

1 0.99 0.69 1.00 1.25 0.72 1.63 1.20 1.09 0.96

time (sec)

N/A 0.969 0.942 0.078 0.057 0.076 0.129 0.117 0.177 22.890

Problem 116

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

102 111 50 99 149 83 158 132 109 120

N.S.

1 1.09 0.49 0.97 1.46 0.81 1.55 1.29 1.07 1.18

time (sec)

N/A 0.647 0.420 0.049 0.058 0.070 0.083 0.133 0.192 0.115

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A F A F B F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

277 277 175 489 0 235 0 546 366 0

N.S.

1 1.00 0.63 1.77 0.00 0.85 0.00 1.97 1.32 0.00

time (sec)

N/A 0.998 1.229 0.113 0.000 0.073 0.000 0.131 0.167 0.000

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A F A F B F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

258 258 163 406 0 353 0 2861 0 0

N.S.

1 1.00 0.63 1.57 0.00 1.37 0.00 11.09 0.00 0.00

time (sec)

N/A 1.000 1.693 0.115 0.000 0.085 0.000 0.162 0.180 0.000

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A F A F B F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

294 294 267 418 0 550 0 1995 0 0

N.S.

1 1.00 0.91 1.42 0.00 1.87 0.00 6.79 0.00 0.00

time (sec)

N/A 1.074 2.448 0.118 0.000 0.087 0.000 0.142 0.226 0.000

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A F B F B F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

396 396 389 511 0 793 0 3178 0 0

N.S.

1 1.00 0.98 1.29 0.00 2.00 0.00 8.03 0.00 0.00

time (sec)

N/A 1.302 2.906 0.164 0.000 0.082 0.000 0.154 0.213 0.000

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A F B F B F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

557 557 669 596 0 1084 0 16988 0 0

N.S.

1 1.00 1.20 1.07 0.00 1.95 0.00 30.50 0.00 0.00

time (sec)

N/A 1.666 2.998 0.261 0.000 0.096 0.000 0.244 0.236 0.000

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A C A A F(-1) F B B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD TBD

size

24 24 25 192 42 32 0 0 26 25

N.S.

1 1.00 1.04 8.00 1.75 1.33 0.00 0.00 1.08 1.04

time (sec)

N/A 0.467 0.315 0.027 0.137 0.095 0.000 0.000 0.169 22.966

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F F(-2) B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 23 25 42 25 0 0 25 23

N.S.

1 1.00 1.05 1.14 1.91 1.14 0.00 0.00 1.14 1.05

time (sec)

N/A 0.440 0.196 83.951 0.140 0.078 0.000 0.000 0.187 23.204

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F F(-2) B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 23 25 42 25 0 0 25 23

N.S.

1 1.00 1.05 1.14 1.91 1.14 0.00 0.00 1.14 1.05

time (sec)

N/A 0.378 0.176 48.674 0.140 0.080 0.000 0.000 0.162 24.071

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F F(-2) B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

20 20 21 23 38 23 0 0 23 21

N.S.

1 1.00 1.05 1.15 1.90 1.15 0.00 0.00 1.15 1.05

time (sec)

N/A 0.315 0.167 26.037 0.131 0.084 0.000 0.000 0.167 23.635

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F F(-2) B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 19 22 36 22 0 0 22 20

N.S.

1 1.00 1.00 1.16 1.89 1.16 0.00 0.00 1.16 1.05

time (sec)

N/A 0.436 0.040 17.519 0.135 0.083 0.000 0.000 0.182 23.026

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F F(-2) B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 23 25 39 25 0 0 25 23

N.S.

1 1.00 1.05 1.14 1.77 1.14 0.00 0.00 1.14 1.05

time (sec)

N/A 0.441 0.322 17.518 0.134 0.079 0.000 0.000 0.171 22.888

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A A A A F F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 23 25 39 25 0 0 25 23

N.S.

1 1.00 1.05 1.14 1.77 1.14 0.00 0.00 1.14 1.05

time (sec)

N/A 0.442 0.315 17.685 0.162 0.084 0.000 0.000 0.186 22.948

Problem 129

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

91 109 45 43 60 43 51 43 44 45

N.S.

1 1.20 0.49 0.47 0.66 0.47 0.56 0.47 0.48 0.49

time (sec)

N/A 0.658 0.191 0.067 0.031 0.069 0.057 0.114 0.164 22.773

Problem 130

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

72 84 37 35 48 35 42 35 36 37

N.S.

1 1.17 0.51 0.49 0.67 0.49 0.58 0.49 0.50 0.51

time (sec)

N/A 0.528 0.161 0.042 0.055 0.066 0.054 0.113 0.170 22.785

Problem 131

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

53 59 29 27 36 27 34 27 28 29

N.S.

1 1.11 0.55 0.51 0.68 0.51 0.64 0.51 0.53 0.55

time (sec)

N/A 0.421 0.150 0.034 0.032 0.065 0.050 0.114 0.179 23.933

Problem 132

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

34 34 21 19 24 19 26 19 20 18

N.S.

1 1.00 0.62 0.56 0.71 0.56 0.76 0.56 0.59 0.53

time (sec)

N/A 0.313 0.118 0.028 0.035 0.066 0.044 0.119 0.160 0.046

Problem 133

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 14 14 14 14 14 15 13

N.S.

1 1.00 1.00 0.88 0.88 0.88 0.88 0.88 0.94 0.81

time (sec)

N/A 0.240 0.036 0.026 0.031 0.061 0.037 0.111 0.185 23.450

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B A A F A F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

27 39 27 57 10 10 0 10 16 0

N.S.

1 1.44 1.00 2.11 0.37 0.37 0.00 0.37 0.59 0.00

time (sec)

N/A 0.364 0.137 0.030 0.092 0.068 0.000 0.117 0.171 0.000

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B A A F A F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

48 60 47 116 13 29 0 29 37 0

N.S.

1 1.25 0.98 2.42 0.27 0.60 0.00 0.60 0.77 0.00

time (sec)

N/A 0.445 0.164 0.036 0.089 0.068 0.000 0.113 0.165 0.000

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B A A F A F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

71 84 56 155 15 38 0 46 55 0

N.S.

1 1.18 0.79 2.18 0.21 0.54 0.00 0.65 0.77 0.00

time (sec)

N/A 0.538 0.190 0.049 0.091 0.064 0.000 0.111 0.177 0.000

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A A A B A A F A F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD TBD

size

92 108 64 189 15 46 0 63 73 0

N.S.

1 1.17 0.70 2.05 0.16 0.50 0.00 0.68 0.79 0.00

time (sec)

N/A 0.645 0.200 0.063 0.088 0.067 0.000 0.109 0.162 0.000

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