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Integrals 201 to 233

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 201

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

117 125 113 0 0 0 0 0 21 0

N.S.

1 1.07 0.97 0.00 0.00 0.00 0.00 0.00 0.18 0.00

time (sec)

N/A 0.627 0.175 0.000 0.000 0.000 0.000 0.000 0.223 0.000

Problem 202

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

144 168 136 0 0 0 0 0 25 0

N.S.

1 1.17 0.94 0.00 0.00 0.00 0.00 0.00 0.17 0.00

time (sec)

N/A 0.697 0.389 0.000 0.000 0.000 0.000 0.000 0.194 0.000

Problem 203

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

74 80 69 135 0 0 0 0 16 0

N.S.

1 1.08 0.93 1.82 0.00 0.00 0.00 0.00 0.22 0.00

time (sec)

N/A 0.469 0.041 0.404 0.000 0.000 0.000 0.000 0.207 0.000

Problem 204

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

52 55 49 99 0 0 0 0 16 0

N.S.

1 1.06 0.94 1.90 0.00 0.00 0.00 0.00 0.31 0.00

time (sec)

N/A 0.359 0.022 0.378 0.000 0.000 0.000 0.000 0.224 0.000

Problem 205

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

30 30 40 69 0 0 0 0 14 0

N.S.

1 1.00 1.33 2.30 0.00 0.00 0.00 0.00 0.47 0.00

time (sec)

N/A 0.250 0.023 0.303 0.000 0.000 0.000 0.000 0.194 0.000

Problem 206

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

11 11 11 24 0 0 0 0 8 0

N.S.

1 1.00 1.00 2.18 0.00 0.00 0.00 0.00 0.73 0.00

time (sec)

N/A 0.169 0.004 0.263 0.000 0.000 0.000 0.000 0.231 0.000

Problem 207

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

14 14 16 14 16 16 12 16 16 16

N.S.

1 1.00 1.14 1.00 1.14 1.14 0.86 1.14 1.14 1.14

time (sec)

N/A 0.191 0.024 0.102 0.064 0.098 0.266 0.104 0.265 0.095

Problem 208

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

14 14 16 14 16 27 14 16 16 16

N.S.

1 1.00 1.14 1.00 1.14 1.93 1.00 1.14 1.14 1.14

time (sec)

N/A 0.188 0.031 0.089 0.061 0.083 0.388 0.108 0.207 0.118

Problem 209

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 14 16 16 15 16 16 16

N.S.

1 1.00 1.12 0.88 1.00 1.00 0.94 1.00 1.00 1.00

time (sec)

N/A 0.194 0.093 0.172 0.069 0.082 2.140 0.115 0.222 0.103

Problem 210

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 14 16 16 15 16 16 16

N.S.

1 1.00 1.12 0.88 1.00 1.00 0.94 1.00 1.00 1.00

time (sec)

N/A 0.195 0.082 0.174 0.073 0.097 0.436 0.108 0.191 0.094

Problem 211

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 14 16 16 15 16 16 16

N.S.

1 1.00 1.12 0.88 1.00 1.00 0.94 1.00 1.00 1.00

time (sec)

N/A 0.194 0.078 0.176 0.062 0.092 0.389 0.107 0.238 0.095

Problem 212

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

93 109 115 161 0 65 0 0 46 0

N.S.

1 1.17 1.24 1.73 0.00 0.70 0.00 0.00 0.49 0.00

time (sec)

N/A 0.585 0.069 0.434 0.000 0.099 0.000 0.000 0.228 0.000

Problem 213

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 Yes Yes N/A TBD TBD TBD TBD TBD TBD

size

71 84 104 0 0 42 0 0 25 0

N.S.

1 1.18 1.46 0.00 0.00 0.59 0.00 0.00 0.35 0.00

time (sec)

N/A 0.454 0.061 0.000 0.000 0.094 0.000 0.000 0.229 0.000

Problem 214

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

30 37 38 36 0 22 0 0 9 0

N.S.

1 1.23 1.27 1.20 0.00 0.73 0.00 0.00 0.30 0.00

time (sec)

N/A 0.280 0.009 0.248 0.000 0.106 0.000 0.000 0.237 0.000

Problem 215

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

15 15 17 15 17 17 14 17 17 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.93 1.13 1.13 1.13

time (sec)

N/A 0.274 0.020 0.185 0.086 0.089 0.419 0.140 0.208 0.154

Problem 216

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

15 15 17 15 17 28 15 17 28 17

N.S.

1 1.00 1.13 1.00 1.13 1.87 1.00 1.13 1.87 1.13

time (sec)

N/A 0.268 0.060 0.077 0.082 0.089 2.104 0.165 0.224 0.152

Problem 217

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 F(-2) N/A N/A

verified

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

size

15 15 17 15 17 17 14 0 17 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.93 0.00 1.13 1.13

time (sec)

N/A 0.191 0.045 0.170 0.059 0.114 0.425 0.000 0.214 0.149

Problem 218

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

82 88 77 112 0 0 0 0 67 0

N.S.

1 1.07 0.94 1.37 0.00 0.00 0.00 0.00 0.82 0.00

time (sec)

N/A 0.487 0.041 0.330 0.000 0.000 0.000 0.000 0.235 0.000

Problem 219

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

58 61 55 74 0 0 0 0 46 0

N.S.

1 1.05 0.95 1.28 0.00 0.00 0.00 0.00 0.79 0.00

time (sec)

N/A 0.366 0.022 0.342 0.000 0.000 0.000 0.000 0.214 0.000

Problem 220

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

34 34 46 36 0 0 0 0 25 0

N.S.

1 1.00 1.35 1.06 0.00 0.00 0.00 0.00 0.74 0.00

time (sec)

N/A 0.265 0.023 0.270 0.000 0.000 0.000 0.000 0.200 0.000

Problem 221

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

13 13 13 14 0 0 0 0 9 0

N.S.

1 1.00 1.00 1.08 0.00 0.00 0.00 0.00 0.69 0.00

time (sec)

N/A 0.185 0.004 0.237 0.000 0.000 0.000 0.000 0.217 0.000

Problem 222

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 F(-2) N/A N/A

verified

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

size

15 15 17 15 17 17 12 0 17 17

N.S.

1 1.00 1.13 1.00 1.13 1.13 0.80 0.00 1.13 1.13

time (sec)

N/A 0.198 0.023 0.083 0.070 0.080 0.221 0.000 0.261 0.194

Problem 223

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 F(-2) N/A N/A

verified

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

size

15 15 17 15 17 28 14 0 28 17

N.S.

1 1.00 1.13 1.00 1.13 1.87 0.93 0.00 1.87 1.13

time (sec)

N/A 0.285 0.027 0.081 0.058 0.086 0.515 0.000 0.215 0.298

Problem 224

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 F(-2) N/A N/A

verified

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

size

15 15 17 15 17 39 14 0 39 17

N.S.

1 1.00 1.13 1.00 1.13 2.60 0.93 0.00 2.60 1.13

time (sec)

N/A 0.393 0.030 0.083 0.069 0.079 0.563 0.000 0.226 0.308

Problem 225

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 F(-2) N/A N/A

verified

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

size

17 17 19 15 17 17 15 0 38 17

N.S.

1 1.00 1.12 0.88 1.00 1.00 0.88 0.00 2.24 1.00

time (sec)

N/A 0.410 0.089 0.197 0.090 0.088 2.111 0.000 0.272 0.182

Problem 226

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 F(-2) N/A N/A

verified

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

size

17 17 19 15 17 17 15 0 16 17

N.S.

1 1.00 1.12 0.88 1.00 1.00 0.88 0.00 0.94 1.00

time (sec)

N/A 0.293 0.068 0.169 0.087 0.095 0.413 0.000 0.195 0.159

Problem 227

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 F(-2) N/A N/A

verified

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

size

17 17 19 15 17 17 15 0 18 17

N.S.

1 1.00 1.12 0.88 1.00 1.00 0.88 0.00 1.06 1.00

time (sec)

N/A 0.200 0.066 0.179 0.067 0.080 0.348 0.000 0.207 0.171

Problem 228

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 F(-2) N/A N/A

verified

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

size

17 17 19 15 17 35 15 0 30 17

N.S.

1 1.00 1.12 0.88 1.00 2.06 0.88 0.00 1.76 1.00

time (sec)

N/A 0.294 0.047 0.168 0.065 0.106 1.296 0.000 0.280 0.163

Problem 229

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

39 44 40 39 0 0 0 0 13 0

N.S.

1 1.13 1.03 1.00 0.00 0.00 0.00 0.00 0.33 0.00

time (sec)

N/A 0.317 0.009 0.251 0.000 0.000 0.000 0.000 0.196 0.000

Problem 230

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

12 12 0 13 0 0 0 0 30 0

N.S.

1 1.00 0.00 1.08 0.00 0.00 0.00 0.00 2.50 0.00

time (sec)

N/A 0.188 0.000 0.434 0.000 0.000 0.000 0.000 0.194 0.000

Problem 231

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

12 12 0 13 0 0 0 0 32 0

N.S.

1 1.00 0.00 1.08 0.00 0.00 0.00 0.00 2.67 0.00

time (sec)

N/A 0.217 0.000 0.448 0.000 0.000 0.000 0.000 0.246 0.000

Problem 232

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

15 15 15 16 0 0 0 15 17 15

N.S.

1 1.00 1.00 1.07 0.00 0.00 0.00 1.00 1.13 1.00

time (sec)

N/A 0.186 0.009 0.151 0.000 0.000 0.000 0.116 0.202 0.147

Problem 233

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Reduce Mupad

grade

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

verified

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

size

15 15 15 16 0 0 0 15 1 15

N.S.

1 1.00 1.00 1.07 0.00 0.00 0.00 1.00 0.07 1.00

time (sec)

N/A 0.193 0.004 0.161 0.000 0.000 0.000 0.116 0.195 0.018

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