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Integrals 101 to 136

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 F F F F F F F(-1)

verified

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

size

128 173 97 0 0 0 0 0 18 0

N.S.

1 1.35 0.76 0.00 0.00 0.00 0.00 0.00 0.14 0.00

time (sec)

N/A 0.607 1.088 0.000 0.000 0.000 0.000 0.000 0.241 0.000

Problem 102

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

119 161 93 0 0 0 0 0 16 0

N.S.

1 1.35 0.78 0.00 0.00 0.00 0.00 0.00 0.13 0.00

time (sec)

N/A 0.548 0.585 0.000 0.000 0.000 0.000 0.000 0.190 0.000

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

55 62 96 56 0 0 0 0 67 0

N.S.

1 1.13 1.75 1.02 0.00 0.00 0.00 0.00 1.22 0.00

time (sec)

N/A 0.286 0.060 1.111 0.000 0.000 0.000 0.000 0.187 0.000

Problem 104

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

122 146 144 0 0 0 0 0 20 0

N.S.

1 1.20 1.18 0.00 0.00 0.00 0.00 0.00 0.16 0.00

time (sec)

N/A 0.592 1.276 0.000 0.000 0.000 0.000 0.000 0.212 0.000

Problem 105

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

130 157 146 0 0 0 0 0 20 0

N.S.

1 1.21 1.12 0.00 0.00 0.00 0.00 0.00 0.15 0.00

time (sec)

N/A 0.588 1.250 0.000 0.000 0.000 0.000 0.000 0.226 0.000

Problem 106

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

167 215 119 0 0 0 0 0 24 0

N.S.

1 1.29 0.71 0.00 0.00 0.00 0.00 0.00 0.14 0.00

time (sec)

N/A 0.674 1.340 0.000 0.000 0.000 0.000 0.000 0.237 0.000

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

96 135 96 0 0 0 0 0 14 0

N.S.

1 1.41 1.00 0.00 0.00 0.00 0.00 0.00 0.15 0.00

time (sec)

N/A 1.092 0.012 0.000 0.000 0.000 0.000 0.000 0.239 0.000

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

12 12 14 12 14 14 14 14 14 14

N.S.

1 1.00 1.17 1.00 1.17 1.17 1.17 1.17 1.17 1.17

time (sec)

N/A 0.544 0.162 0.231 0.101 0.078 3.314 0.114 0.226 4.107

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

10 10 10 9 0 0 7 0 8 0

N.S.

1 1.00 1.00 0.90 0.00 0.00 0.70 0.00 0.80 0.00

time (sec)

N/A 0.190 0.004 0.306 0.000 0.000 0.208 0.000 0.192 0.000

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

25 25 25 22 0 0 0 0 11 0

N.S.

1 1.00 1.00 0.88 0.00 0.00 0.00 0.00 0.44 0.00

time (sec)

N/A 0.314 0.014 0.366 0.000 0.000 0.000 0.000 0.188 0.000

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

61 66 46 46 0 0 0 0 12 0

N.S.

1 1.08 0.75 0.75 0.00 0.00 0.00 0.00 0.20 0.00

time (sec)

N/A 0.479 0.035 0.734 0.000 0.000 0.000 0.000 0.208 0.000

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

90 139 64 68 0 0 0 0 14 0

N.S.

1 1.54 0.71 0.76 0.00 0.00 0.00 0.00 0.16 0.00

time (sec)

N/A 0.878 0.052 0.948 0.000 0.000 0.000 0.000 0.241 0.000

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

142 213 94 103 0 0 0 0 14 0

N.S.

1 1.50 0.66 0.73 0.00 0.00 0.00 0.00 0.10 0.00

time (sec)

N/A 1.278 0.071 1.240 0.000 0.000 0.000 0.000 0.196 0.000

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

12 12 14 12 14 14 14 14 14 14

N.S.

1 1.00 1.17 1.00 1.17 1.17 1.17 1.17 1.17 1.17

time (sec)

N/A 1.013 0.337 0.234 0.130 0.077 3.895 0.121 0.195 3.882

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

44 54 44 0 0 0 0 0 14 0

N.S.

1 1.23 1.00 0.00 0.00 0.00 0.00 0.00 0.32 0.00

time (sec)

N/A 0.532 0.008 0.000 0.000 0.000 0.000 0.000 0.235 0.000

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

12 12 14 12 14 14 12 14 14 14

N.S.

1 1.00 1.17 1.00 1.17 1.17 1.00 1.17 1.17 1.17

time (sec)

N/A 0.197 0.188 0.279 0.103 0.089 3.768 0.110 0.199 3.879

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

34 34 36 28 0 0 0 0 11 0

N.S.

1 1.00 1.06 0.82 0.00 0.00 0.00 0.00 0.32 0.00

time (sec)

N/A 0.281 0.014 0.641 0.000 0.000 0.000 0.000 0.192 0.000

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

62 70 44 46 0 0 0 0 12 0

N.S.

1 1.13 0.71 0.74 0.00 0.00 0.00 0.00 0.19 0.00

time (sec)

N/A 0.491 0.054 0.756 0.000 0.000 0.000 0.000 0.202 0.000

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

109 129 72 78 0 0 0 0 14 0

N.S.

1 1.18 0.66 0.72 0.00 0.00 0.00 0.00 0.13 0.00

time (sec)

N/A 0.748 0.071 0.823 0.000 0.000 0.000 0.000 0.223 0.000

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

146 233 94 104 0 0 0 0 14 0

N.S.

1 1.60 0.64 0.71 0.00 0.00 0.00 0.00 0.10 0.00

time (sec)

N/A 1.466 0.072 1.025 0.000 0.000 0.000 0.000 0.189 0.000

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

29 34 27 24 0 0 0 0 11 0

N.S.

1 1.17 0.93 0.83 0.00 0.00 0.00 0.00 0.38 0.00

time (sec)

N/A 0.278 0.021 1.036 0.000 0.000 0.000 0.000 0.189 0.000

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

29 34 27 24 0 0 0 0 11 0

N.S.

1 1.17 0.93 0.83 0.00 0.00 0.00 0.00 0.38 0.00

time (sec)

N/A 0.298 0.020 1.102 0.000 0.000 0.000 0.000 0.207 0.000

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

201 238 134 198 0 0 0 0 18 0

N.S.

1 1.18 0.67 0.99 0.00 0.00 0.00 0.00 0.09 0.00

time (sec)

N/A 2.026 0.269 1.883 0.000 0.000 0.000 0.000 0.206 0.000

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

109 114 78 97 0 0 0 0 16 0

N.S.

1 1.05 0.72 0.89 0.00 0.00 0.00 0.00 0.15 0.00

time (sec)

N/A 0.909 0.130 1.174 0.000 0.000 0.000 0.000 0.210 0.000

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

46 46 45 38 0 0 0 0 15 0

N.S.

1 1.00 0.98 0.83 0.00 0.00 0.00 0.00 0.33 0.00

time (sec)

N/A 0.328 0.021 0.685 0.000 0.000 0.000 0.000 0.203 0.000

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 18 18 15 18 18 18

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.94 1.12 1.12 1.12

time (sec)

N/A 0.294 0.487 0.309 0.186 0.079 1.240 0.108 0.239 4.087

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

174 211 123 175 0 0 0 0 18 0

N.S.

1 1.21 0.71 1.01 0.00 0.00 0.00 0.00 0.10 0.00

time (sec)

N/A 1.953 0.188 2.614 0.000 0.000 0.000 0.000 0.211 0.000

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

97 104 73 84 0 0 0 0 16 0

N.S.

1 1.07 0.75 0.87 0.00 0.00 0.00 0.00 0.16 0.00

time (sec)

N/A 0.943 0.118 1.536 0.000 0.000 0.000 0.000 0.200 0.000

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

33 33 32 30 0 0 0 0 15 0

N.S.

1 1.00 0.97 0.91 0.00 0.00 0.00 0.00 0.45 0.00

time (sec)

N/A 0.347 0.013 0.754 0.000 0.000 0.000 0.000 0.203 0.000

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 18 18 15 18 39 18

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.94 1.12 2.44 1.12

time (sec)

N/A 0.247 0.370 0.289 0.155 0.089 1.262 0.108 0.222 4.007

Problem 131

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

371 378 322 0 0 0 0 0 16 0

N.S.

1 1.02 0.87 0.00 0.00 0.00 0.00 0.00 0.04 0.00

time (sec)

N/A 1.797 2.403 0.000 0.000 0.000 0.000 0.000 0.206 0.000

Problem 132

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

153 160 107 0 0 0 0 0 15 0

N.S.

1 1.05 0.70 0.00 0.00 0.00 0.00 0.00 0.10 0.00

time (sec)

N/A 0.510 0.655 0.000 0.000 0.000 0.000 0.000 0.205 0.000

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 18 18 15 18 18 18

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.94 1.12 1.12 1.12

time (sec)

N/A 0.287 2.869 0.618 0.182 0.085 0.965 0.106 0.244 4.106

Problem 134

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

371 378 293 0 0 0 0 0 16 0

N.S.

1 1.02 0.79 0.00 0.00 0.00 0.00 0.00 0.04 0.00

time (sec)

N/A 1.453 2.079 0.000 0.000 0.000 0.000 0.000 0.215 0.000

Problem 135

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

153 160 137 0 0 0 0 0 15 0

N.S.

1 1.05 0.90 0.00 0.00 0.00 0.00 0.00 0.10 0.00

time (sec)

N/A 0.523 0.369 0.000 0.000 0.000 0.000 0.000 0.187 0.000

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 18 18 15 18 18 18

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.94 1.12 1.12 1.12

time (sec)

N/A 0.255 2.675 0.641 0.179 0.094 0.924 0.108 0.183 4.388

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