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2.2.1 Integrals 1 to 49

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 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F B

verified

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

size

62 72 56 0 0 0 0 0 58

N.S.

1 1.16 0.90 0.00 0.00 0.00 0.00 0.00 0.94

time (sec)

N/A 0.471 0.037 0.000 0.000 0.000 0.000 0.000 0.894

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 59 40 40 66 32 119 152 0

N.S.

1 1.02 0.69 0.69 1.14 0.55 2.05 2.62 0.00

time (sec)

N/A 0.220 0.020 0.250 0.189 0.258 63.927 0.292 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 50 35 35 52 27 90 116 0

N.S.

1 1.06 0.74 0.74 1.11 0.57 1.91 2.47 0.00

time (sec)

N/A 0.214 0.018 0.194 0.191 0.254 19.272 0.287 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 39 27 28 38 20 61 80 0

N.S.

1 1.08 0.75 0.78 1.06 0.56 1.69 2.22 0.00

time (sec)

N/A 0.201 0.016 0.235 0.195 0.265 5.871 0.283 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 21 20 12 29 41 20

N.S.

1 1.00 1.00 1.31 1.25 0.75 1.81 2.56 1.25

time (sec)

N/A 0.166 0.002 0.233 0.215 0.254 2.010 0.282 1.271

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

56 62 54 105 0 0 0 0 42

N.S.

1 1.11 0.96 1.88 0.00 0.00 0.00 0.00 0.75

time (sec)

N/A 0.474 0.039 0.812 0.000 0.000 0.000 0.000 1.056

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 39 32 44 51 21 76 32 28

N.S.

1 1.03 0.84 1.16 1.34 0.55 2.00 0.84 0.74

time (sec)

N/A 0.203 0.020 0.250 0.267 0.267 12.862 0.271 0.852

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 57 55 57 80 30 146 59 0

N.S.

1 1.06 1.02 1.06 1.48 0.56 2.70 1.09 0.00

time (sec)

N/A 0.208 0.035 0.252 0.270 0.256 42.491 0.271 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 62 42 56 54 39 51 68 0

N.S.

1 1.11 0.75 1.00 0.96 0.70 0.91 1.21 0.00

time (sec)

N/A 0.270 0.026 1.767 0.264 0.250 0.178 0.277 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 57 44 67 46 38 41 48 38

N.S.

1 1.21 0.94 1.43 0.98 0.81 0.87 1.02 0.81

time (sec)

N/A 0.236 0.023 1.760 0.266 0.246 0.147 0.276 0.773

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 25 27 23 26 22 26 23

N.S.

1 1.00 1.00 1.08 0.92 1.04 0.88 1.04 0.92

time (sec)

N/A 0.205 0.007 1.744 0.184 0.252 0.135 0.269 0.110

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F F F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 67 54 125 0 0 0 0 49

N.S.

1 1.14 0.92 2.12 0.00 0.00 0.00 0.00 0.83

time (sec)

N/A 0.385 0.033 2.609 0.000 0.000 0.000 0.000 0.773

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 93 31 52 65 27 61 30

N.S.

1 1.00 2.91 0.97 1.62 2.03 0.84 1.91 0.94

time (sec)

N/A 0.241 0.104 0.085 0.198 0.283 1.148 0.284 0.727

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 35 33 32 38 51 61 0

N.S.

1 1.00 0.92 0.87 0.84 1.00 1.34 1.61 0.00

time (sec)

N/A 0.229 0.020 1.472 0.275 0.272 0.667 0.294 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 61 69 54 64 92 99 80 0

N.S.

1 1.02 1.15 0.90 1.07 1.53 1.65 1.33 0.00

time (sec)

N/A 0.251 0.040 1.459 0.285 0.276 1.411 0.273 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F F(-2) F F F(-1)

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

69 81 63 155 0 0 0 0 0

N.S.

1 1.17 0.91 2.25 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.501 0.062 1.380 0.000 0.000 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

197 207 174 329 0 151 0 408 0

N.S.

1 1.05 0.88 1.67 0.00 0.77 0.00 2.07 0.00

time (sec)

N/A 0.727 0.139 0.385 0.000 0.283 0.000 0.300 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

155 158 149 248 0 129 0 300 0

N.S.

1 1.02 0.96 1.60 0.00 0.83 0.00 1.94 0.00

time (sec)

N/A 0.514 0.187 0.312 0.000 0.275 0.000 0.297 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 117 129 193 0 117 0 203 0

N.S.

1 1.01 1.11 1.66 0.00 1.01 0.00 1.75 0.00

time (sec)

N/A 0.382 0.137 0.314 0.000 0.283 0.000 0.293 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 78 110 106 0 102 0 134 0

N.S.

1 0.99 1.39 1.34 0.00 1.29 0.00 1.70 0.00

time (sec)

N/A 0.412 0.087 0.319 0.000 0.289 0.000 0.290 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

36 34 469 43 55 75 0 81 33

N.S.

1 0.94 13.03 1.19 1.53 2.08 0.00 2.25 0.92

time (sec)

N/A 0.223 0.395 0.079 0.190 0.269 0.000 0.299 1.015

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

210 266 375 607 0 0 0 0 0

N.S.

1 1.27 1.79 2.89 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.104 0.353 1.871 0.000 0.000 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 76 115 127 0 278 0 96 0

N.S.

1 1.10 1.67 1.84 0.00 4.03 0.00 1.39 0.00

time (sec)

N/A 0.418 0.281 0.705 0.000 0.318 0.000 0.311 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 154 199 319 0 428 0 217 0

N.S.

1 1.25 1.62 2.59 0.00 3.48 0.00 1.76 0.00

time (sec)

N/A 0.764 0.545 0.711 0.000 0.313 0.000 0.353 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

180 228 241 528 0 548 0 450 0

N.S.

1 1.27 1.34 2.93 0.00 3.04 0.00 2.50 0.00

time (sec)

N/A 1.060 0.334 0.720 0.000 0.319 0.000 0.366 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

239 305 307 795 0 673 0 841 0

N.S.

1 1.28 1.28 3.33 0.00 2.82 0.00 3.52 0.00

time (sec)

N/A 1.432 0.360 0.720 0.000 0.365 0.000 0.374 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F F F F(-2) F(-1)

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

366 342 453 703 0 0 0 0 0

N.S.

1 0.93 1.24 1.92 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.591 3.950 1.530 0.000 0.000 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

272 255 347 500 0 0 0 0 0

N.S.

1 0.94 1.28 1.84 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.558 4.462 1.421 0.000 0.000 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

145 137 213 212 0 0 0 0 0

N.S.

1 0.94 1.47 1.46 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.437 0.699 0.987 0.000 0.000 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

86 77 99 150 0 0 0 0 0

N.S.

1 0.90 1.15 1.74 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.422 0.109 0.523 0.000 0.000 0.000 0.000 0.000

Problem 31

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

324 395 408 0 0 0 0 0 0

N.S.

1 1.22 1.26 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.626 0.289 0.000 0.000 0.000 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

254 258 802 302 0 0 0 0 0

N.S.

1 1.02 3.16 1.19 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.747 2.494 1.638 0.000 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

464 420 656 749 0 0 0 0 0

N.S.

1 0.91 1.41 1.61 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.722 7.179 1.487 0.000 0.000 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

264 241 314 425 0 0 0 0 0

N.S.

1 0.91 1.19 1.61 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.573 0.622 1.246 0.000 0.000 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

140 131 162 224 0 0 0 0 0

N.S.

1 0.94 1.16 1.60 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.556 0.087 0.860 0.000 0.000 0.000 0.000 0.000

Problem 36

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

448 530 554 0 0 0 0 0 0

N.S.

1 1.18 1.24 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.894 0.282 0.000 0.000 0.000 0.000 0.000 0.000

Problem 37

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

378 381 289 0 0 0 0 0 0

N.S.

1 1.01 0.76 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.946 0.339 0.000 0.000 0.000 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

48 44 127 54 63 88 0 91 44

N.S.

1 0.92 2.65 1.12 1.31 1.83 0.00 1.90 0.92

time (sec)

N/A 0.295 0.137 0.226 0.181 0.276 0.000 0.336 1.188

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

48 44 130 0 66 94 0 74 42

N.S.

1 0.92 2.71 0.00 1.38 1.96 0.00 1.54 0.88

time (sec)

N/A 0.316 0.197 0.000 0.182 0.305 0.000 0.332 0.894

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

85 101 280 188 0 0 0 0 91

N.S.

1 1.19 3.29 2.21 0.00 0.00 0.00 0.00 1.07

time (sec)

N/A 0.471 0.418 1.849 0.000 0.000 0.000 0.000 1.448

Problem 41

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

95 94 79 0 0 0 0 0 0

N.S.

1 0.99 0.83 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.342 0.332 0.000 0.000 0.000 0.000 0.000 0.000

Problem 42

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

87 86 101 0 0 0 0 0 0

N.S.

1 0.99 1.16 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.321 0.193 0.000 0.000 0.000 0.000 0.000 0.000

Problem 43

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

87 86 54 0 0 0 0 0 0

N.S.

1 0.99 0.62 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.302 0.072 0.000 0.000 0.000 0.000 0.000 0.000

Problem 44

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

43 43 75 0 0 0 0 0 0

N.S.

1 1.00 1.74 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.278 0.046 0.000 0.000 0.000 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

39 44 33 0 0 23 0 42 0

N.S.

1 1.13 0.85 0.00 0.00 0.59 0.00 1.08 0.00

time (sec)

N/A 0.231 0.029 0.000 0.000 0.263 0.000 0.279 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

41 42 30 0 0 32 0 0 0

N.S.

1 1.02 0.73 0.00 0.00 0.78 0.00 0.00 0.00

time (sec)

N/A 0.283 0.031 0.000 0.000 0.280 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

84 80 54 0 0 41 0 0 0

N.S.

1 0.95 0.64 0.00 0.00 0.49 0.00 0.00 0.00

time (sec)

N/A 0.287 0.105 0.000 0.000 0.295 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

81 74 50 0 0 51 0 0 0

N.S.

1 0.91 0.62 0.00 0.00 0.63 0.00 0.00 0.00

time (sec)

N/A 0.285 0.117 0.000 0.000 0.307 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

69 77 59 167 0 0 0 114 0

N.S.

1 1.12 0.86 2.42 0.00 0.00 0.00 1.65 0.00

time (sec)

N/A 0.488 0.059 1.198 0.000 0.000 0.000 0.502 0.000

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