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2.2.2 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 Mupad

grade

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

verified

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

size

133 152 102 0 0 448 0 0 0

N.S.

1 1.14 0.77 0.00 0.00 3.37 0.00 0.00 0.00

time (sec)

N/A 0.568 1.149 0.000 0.000 0.278 0.000 0.000 0.000

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

124 141 98 0 0 445 0 0 0

N.S.

1 1.14 0.79 0.00 0.00 3.59 0.00 0.00 0.00

time (sec)

N/A 0.542 1.111 0.000 0.000 0.286 0.000 0.000 0.000

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 55 96 56 82 121 0 0 0

N.S.

1 1.00 1.75 1.02 1.49 2.20 0.00 0.00 0.00

time (sec)

N/A 0.277 0.060 1.046 0.196 0.264 0.000 0.000 0.000

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

127 143 102 0 0 444 0 0 0

N.S.

1 1.13 0.80 0.00 0.00 3.50 0.00 0.00 0.00

time (sec)

N/A 0.586 1.163 0.000 0.000 0.276 0.000 0.000 0.000

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

135 154 105 0 0 460 0 0 0

N.S.

1 1.14 0.78 0.00 0.00 3.41 0.00 0.00 0.00

time (sec)

N/A 0.588 1.131 0.000 0.000 0.292 0.000 0.000 0.000

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

172 240 124 0 0 689 0 0 0

N.S.

1 1.40 0.72 0.00 0.00 4.01 0.00 0.00 0.00

time (sec)

N/A 0.663 2.070 0.000 0.000 0.287 0.000 0.000 0.000

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

12 12 14 12 14 14 14 14 14

N.S.

1 1.00 1.17 1.00 1.17 1.17 1.17 1.17 1.17

time (sec)

N/A 1.078 1.058 0.210 0.258 0.253 2.457 0.259 5.558

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

44 48 44 0 0 0 0 0 0

N.S.

1 1.09 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.529 0.009 0.000 0.000 0.000 0.000 0.000 0.000

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

12 12 14 12 14 14 12 14 14

N.S.

1 1.00 1.17 1.00 1.17 1.17 1.00 1.17 1.17

time (sec)

N/A 0.198 1.454 0.212 0.264 0.251 2.120 0.267 5.148

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 34 37 29 0 145 0 0 0

N.S.

1 0.97 1.06 0.83 0.00 4.14 0.00 0.00 0.00

time (sec)

N/A 0.293 0.016 0.525 0.000 0.261 0.000 0.000 0.000

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 69 44 45 0 219 0 0 0

N.S.

1 1.11 0.71 0.73 0.00 3.53 0.00 0.00 0.00

time (sec)

N/A 0.481 0.038 0.725 0.000 0.275 0.000 0.000 0.000

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 129 72 91 0 296 0 0 0

N.S.

1 1.16 0.65 0.82 0.00 2.67 0.00 0.00 0.00

time (sec)

N/A 0.744 0.060 0.752 0.000 0.293 0.000 0.000 0.000

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 232 94 111 0 361 0 0 0

N.S.

1 1.58 0.64 0.76 0.00 2.46 0.00 0.00 0.00

time (sec)

N/A 1.421 0.074 1.460 0.000 0.297 0.000 0.000 0.000

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

97 127 97 0 0 0 0 0 0

N.S.

1 1.31 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.043 0.013 0.000 0.000 0.000 0.000 0.000 0.000

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

12 12 13 12 14 14 14 14 14

N.S.

1 1.00 1.08 1.00 1.17 1.17 1.17 1.17 1.17

time (sec)

N/A 0.469 0.026 0.215 0.292 0.265 1.973 0.286 5.382

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 10 9 0 0 7 0 0

N.S.

1 1.00 1.00 0.90 0.00 0.00 0.70 0.00 0.00

time (sec)

N/A 0.183 0.004 0.275 0.000 0.000 0.215 0.000 0.000

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 25 22 0 143 0 0 0

N.S.

1 1.00 1.00 0.88 0.00 5.72 0.00 0.00 0.00

time (sec)

N/A 0.290 0.013 0.410 0.000 0.278 0.000 0.000 0.000

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 66 42 44 0 221 0 0 0

N.S.

1 1.10 0.70 0.73 0.00 3.68 0.00 0.00 0.00

time (sec)

N/A 0.452 0.035 0.768 0.000 0.269 0.000 0.000 0.000

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 138 64 66 0 297 0 0 0

N.S.

1 1.55 0.72 0.74 0.00 3.34 0.00 0.00 0.00

time (sec)

N/A 0.818 0.063 1.047 0.000 0.287 0.000 0.000 0.000

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 214 93 116 0 361 0 0 0

N.S.

1 1.51 0.65 0.82 0.00 2.54 0.00 0.00 0.00

time (sec)

N/A 1.217 0.076 1.504 0.000 0.280 0.000 0.000 0.000

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 34 23 24 0 84 0 0 0

N.S.

1 1.17 0.79 0.83 0.00 2.90 0.00 0.00 0.00

time (sec)

N/A 0.264 0.020 1.087 0.000 0.280 0.000 0.000 0.000

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 34 27 24 0 86 0 0 0

N.S.

1 1.17 0.93 0.83 0.00 2.97 0.00 0.00 0.00

time (sec)

N/A 0.264 0.020 1.150 0.000 0.270 0.000 0.000 0.000

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

220 240 134 217 0 414 0 0 0

N.S.

1 1.09 0.61 0.99 0.00 1.88 0.00 0.00 0.00

time (sec)

N/A 1.988 0.244 2.426 0.000 0.295 0.000 0.000 0.000

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 114 76 96 0 274 0 0 0

N.S.

1 1.05 0.70 0.88 0.00 2.51 0.00 0.00 0.00

time (sec)

N/A 0.845 0.131 1.488 0.000 0.281 0.000 0.000 0.000

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 46 39 0 161 0 0 0

N.S.

1 1.00 0.98 0.83 0.00 3.43 0.00 0.00 0.00

time (sec)

N/A 0.331 0.019 0.865 0.000 0.269 0.000 0.000 0.000

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

16 16 18 16 18 18 15 18 18

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.94 1.12 1.12

time (sec)

N/A 0.289 3.232 0.254 0.287 0.259 1.057 0.272 7.003

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

185 211 123 170 0 414 0 0 0

N.S.

1 1.14 0.66 0.92 0.00 2.24 0.00 0.00 0.00

time (sec)

N/A 1.843 0.219 4.124 0.000 0.286 0.000 0.000 0.000

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 105 69 82 0 276 0 0 0

N.S.

1 1.09 0.72 0.85 0.00 2.88 0.00 0.00 0.00

time (sec)

N/A 0.944 0.118 2.294 0.000 0.292 0.000 0.000 0.000

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 33 32 30 0 159 0 0 0

N.S.

1 1.00 0.97 0.91 0.00 4.82 0.00 0.00 0.00

time (sec)

N/A 0.329 0.017 1.062 0.000 0.262 0.000 0.000 0.000

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

16 16 18 16 18 18 15 18 18

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.94 1.12 1.12

time (sec)

N/A 0.264 1.393 0.263 0.371 0.264 0.976 0.275 6.028

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

371 377 320 1242 0 451 0 0 0

N.S.

1 1.02 0.86 3.35 0.00 1.22 0.00 0.00 0.00

time (sec)

N/A 1.745 4.569 2.364 0.000 0.285 0.000 0.000 0.000

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

154 160 144 272 0 239 0 0 0

N.S.

1 1.04 0.94 1.77 0.00 1.55 0.00 0.00 0.00

time (sec)

N/A 0.490 0.868 1.498 0.000 0.259 0.000 0.000 0.000

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

16 16 18 16 18 18 15 18 18

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.94 1.12 1.12

time (sec)

N/A 0.290 14.914 0.348 0.385 0.253 0.712 0.298 5.884

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

370 378 393 1244 0 453 0 0 0

N.S.

1 1.02 1.06 3.36 0.00 1.22 0.00 0.00 0.00

time (sec)

N/A 1.452 2.036 3.237 0.000 0.281 0.000 0.000 0.000

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 160 153 274 0 239 0 0 0

N.S.

1 1.05 1.00 1.79 0.00 1.56 0.00 0.00 0.00

time (sec)

N/A 0.494 0.882 1.926 0.000 0.265 0.000 0.000 0.000

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

size

16 16 18 16 18 18 15 18 18

N.S.

1 1.00 1.12 1.00 1.12 1.12 0.94 1.12 1.12

time (sec)

N/A 0.259 9.195 0.345 0.367 0.254 0.692 0.268 5.202

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