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2.2.3 Integrals 201 to 249

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.

Problem 201

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 51 0 0 0 0 0 -1

N.S.

1 1.00 1.28 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.023 0.007 0.014 0.000 0.000 0.000 0.000 0.000

Problem 202

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

26 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.021 0.032 0.018 0.000 0.000 0.000 0.000 0.000

Problem 203

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

64 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.047 0.034 0.018 0.000 0.000 0.000 0.000 0.000

Problem 204

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

103 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.076 0.035 0.017 0.000 0.000 0.000 0.000 0.000

Problem 205

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F A F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

20 20 20 0 0 0 15 0 -1

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.75 0.00 -0.05

time (sec)

N/A 0.016 0.003 0.008 0.000 0.000 1.135 0.000 0.000

Problem 206

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

33 33 33 0 0 0 0 0 -1

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.029 0.004 0.013 0.000 0.000 0.000 0.000 0.000

Problem 207

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F F F F F

verified

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

size

26 26 0 0 0 0 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04

time (sec)

N/A 0.074 0.073 0.027 0.000 0.000 0.000 0.000 0.000

Problem 208

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A A F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

217 217 196 0 0 230 250 0 -1

N.S.

1 1.00 0.90 0.00 0.00 1.06 1.15 0.00 -0.00

time (sec)

N/A 0.129 0.391 0.036 0.000 0.360 76.595 0.000 0.000

Problem 209

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A A F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

185 185 168 0 0 196 206 0 -1

N.S.

1 1.00 0.91 0.00 0.00 1.06 1.11 0.00 -0.01

time (sec)

N/A 0.098 0.243 0.036 0.000 0.373 24.940 0.000 0.000

Problem 210

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A A F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 113 0 0 146 136 0 -1

N.S.

1 1.00 1.07 0.00 0.00 1.38 1.28 0.00 -0.01

time (sec)

N/A 0.079 0.058 0.033 0.000 0.355 6.964 0.000 0.000

Problem 211

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F A F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

26 26 30 0 0 0 26 0 -1

N.S.

1 1.00 1.15 0.00 0.00 0.00 1.00 0.00 -0.04

time (sec)

N/A 0.020 0.007 0.035 0.000 0.000 9.093 0.000 0.000

Problem 212

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 115 0 0 144 0 0 -1

N.S.

1 1.00 0.81 0.00 0.00 1.01 0.00 0.00 -0.01

time (sec)

N/A 0.078 0.121 0.052 0.000 0.388 0.000 0.000 0.000

Problem 213

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

202 202 163 0 0 182 0 0 -1

N.S.

1 1.00 0.81 0.00 0.00 0.90 0.00 0.00 -0.00

time (sec)

N/A 0.111 0.155 0.067 0.000 0.385 0.000 0.000 0.000

Problem 214

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F A F F F(-1)

verified

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

size

253 253 0 0 0 274 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 1.08 0.00 0.00 -0.00

time (sec)

N/A 0.176 0.104 0.022 0.000 0.380 0.000 0.000 0.000

Problem 215

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F A F F F(-1)

verified

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

size

221 221 0 0 0 241 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 1.09 0.00 0.00 -0.00

time (sec)

N/A 0.130 0.087 0.019 0.000 0.357 0.000 0.000 0.000

Problem 216

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F A F F F(-1)

verified

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

size

131 131 0 0 0 184 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 1.40 0.00 0.00 -0.01

time (sec)

N/A 0.090 0.068 0.017 0.000 0.367 0.000 0.000 0.000

Problem 217

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F A F F(-1)

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

26 26 30 0 0 0 26 0 -1

N.S.

1 1.00 1.15 0.00 0.00 0.00 1.00 0.00 -0.04

time (sec)

N/A 0.020 0.006 0.019 0.000 0.000 5.105 0.000 0.000

Problem 218

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F A F F F(-1)

verified

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

size

174 174 0 0 0 167 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.96 0.00 0.00 -0.01

time (sec)

N/A 0.110 0.108 0.033 0.000 0.409 0.000 0.000 0.000

Problem 219

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F A F F F(-1)

verified

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

size

238 238 0 0 0 217 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.91 0.00 0.00 -0.00

time (sec)

N/A 0.159 0.091 0.049 0.000 0.365 0.000 0.000 0.000

Problem 220

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

30 0 266 844 0 0 0 0 -1

N.S.

1 0.00 8.87 28.13 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.016 0.144 0.399 0.000 0.000 0.000 0.000 0.000

Problem 221

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

178 0 0 867 0 0 0 0 -1

N.S.

1 0.00 0.00 4.87 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.076 0.077 0.212 0.000 0.000 0.000 0.000 0.000

Problem 222

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

245 0 0 1065 0 0 0 0 -1

N.S.

1 0.00 0.00 4.35 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.147 0.038 0.860 0.000 0.000 0.000 0.000 0.000

Problem 223

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 27 0 23 32 22 32 23

N.S.

1 1.00 1.00 0.00 0.85 1.19 0.81 1.19 0.85

time (sec)

N/A 0.021 0.004 0.018 0.276 0.339 0.407 3.532 3.838

Problem 224

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 27 0 23 32 22 32 23

N.S.

1 1.00 1.00 0.00 0.85 1.19 0.81 1.19 0.85

time (sec)

N/A 0.012 0.002 0.014 0.282 0.347 0.217 4.566 3.799

Problem 225

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

18 18 18 19 18 21 15 21 17

N.S.

1 1.00 1.00 1.06 1.00 1.17 0.83 1.17 0.94

time (sec)

N/A 0.005 0.002 0.023 0.286 0.355 0.116 5.823 0.027

Problem 226

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 22 21 20 19 37 20 20

N.S.

1 1.00 1.00 0.95 0.91 0.86 1.68 0.91 0.91

time (sec)

N/A 0.020 0.003 0.030 0.284 0.351 1.004 3.755 3.801

Problem 227

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

23 23 23 0 23 20 17 25 19

N.S.

1 1.00 1.00 0.00 1.00 0.87 0.74 1.09 0.83

time (sec)

N/A 0.020 0.002 0.013 0.281 0.338 0.222 6.393 3.881

Problem 228

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 27 0 23 24 24 28 23

N.S.

1 1.00 1.00 0.00 0.85 0.89 0.89 1.04 0.85

time (sec)

N/A 0.020 0.002 0.014 0.284 0.333 0.485 5.651 3.842

Problem 229

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 27 0 23 24 24 28 23

N.S.

1 1.00 1.00 0.00 0.85 0.89 0.89 1.04 0.85

time (sec)

N/A 0.020 0.002 0.014 0.285 0.364 0.893 3.015 3.868

Problem 230

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

52 52 52 0 46 113 49 115 46

N.S.

1 1.00 1.00 0.00 0.88 2.17 0.94 2.21 0.88

time (sec)

N/A 0.050 0.004 0.014 0.294 0.345 0.799 5.444 3.798

Problem 231

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

52 52 43 0 46 113 46 112 46

N.S.

1 1.00 0.83 0.00 0.88 2.17 0.88 2.15 0.88

time (sec)

N/A 0.029 0.006 0.015 0.273 0.337 0.417 7.380 3.848

Problem 232

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 37 0 39 90 39 92 39

N.S.

1 1.00 0.95 0.00 1.00 2.31 1.00 2.36 1.00

time (sec)

N/A 0.015 0.004 0.013 0.283 0.353 0.218 4.761 3.844

Problem 233

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 22 21 20 54 41 59 20

N.S.

1 1.00 1.00 0.95 0.91 2.45 1.86 2.68 0.91

time (sec)

N/A 0.032 0.002 0.030 0.271 0.423 0.778 5.350 3.749

Problem 234

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 40 0 46 81 41 90 40

N.S.

1 1.00 0.87 0.00 1.00 1.76 0.89 1.96 0.87

time (sec)

N/A 0.047 0.005 0.014 0.272 0.412 0.223 2.838 3.851

Problem 235

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

52 52 43 0 46 87 48 94 46

N.S.

1 1.00 0.83 0.00 0.88 1.67 0.92 1.81 0.88

time (sec)

N/A 0.047 0.005 0.015 0.276 0.337 0.489 5.073 3.785

Problem 236

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

52 52 52 0 46 88 51 95 46

N.S.

1 1.00 1.00 0.00 0.88 1.69 0.98 1.83 0.88

time (sec)

N/A 0.047 0.003 0.014 0.279 0.335 0.894 4.673 3.881

Problem 237

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

135 135 91 0 285 1355 0 1811 -1

N.S.

1 1.00 0.67 0.00 2.11 10.04 0.00 13.41 -0.01

time (sec)

N/A 0.153 0.043 0.030 0.290 0.354 0.000 4.388 0.000

Problem 238

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

93 93 90 0 152 388 0 561 -1

N.S.

1 1.00 0.97 0.00 1.63 4.17 0.00 6.03 -0.01

time (sec)

N/A 0.085 0.032 0.030 0.279 0.391 0.000 3.118 0.000

Problem 239

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 37 0 63 69 110 111 -1

N.S.

1 1.00 0.73 0.00 1.24 1.35 2.16 2.18 -0.02

time (sec)

N/A 0.032 0.012 0.029 0.282 0.373 4.273 4.958 0.000

Problem 240

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

86 86 85 0 0 104 0 140 -1

N.S.

1 1.00 0.99 0.00 0.00 1.21 0.00 1.63 -0.01

time (sec)

N/A 0.127 0.105 0.029 0.000 0.368 0.000 3.626 0.000

Problem 241

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

127 127 112 0 0 198 0 1540 -1

N.S.

1 1.00 0.88 0.00 0.00 1.56 0.00 12.13 -0.01

time (sec)

N/A 0.167 0.190 0.028 0.000 0.375 0.000 4.486 0.000

Problem 242

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F(-2) F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

134 134 133 0 0 0 0 0 -1

N.S.

1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.131 0.167 0.126 0.000 0.000 0.000 0.000 0.000

Problem 243

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F(-2) F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 117 0 0 0 0 0 -1

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.111 0.129 0.030 0.000 0.000 0.000 0.000 0.000

Problem 244

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F(-2) F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 117 0 0 0 0 0 -1

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.088 0.120 0.031 0.000 0.000 0.000 0.000 0.000

Problem 245

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F(-2) A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

108 108 108 0 0 73 0 0 -1

N.S.

1 1.00 1.00 0.00 0.00 0.68 0.00 0.00 -0.01

time (sec)

N/A 0.065 0.108 0.028 0.000 0.094 0.000 0.000 0.000

Problem 246

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

33 33 33 34 33 49 80 36 33

N.S.

1 1.00 1.00 1.03 1.00 1.48 2.42 1.09 1.00

time (sec)

N/A 0.059 0.008 0.045 0.286 0.379 1.460 5.620 4.072

Problem 247

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F(-2) F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

107 107 107 0 0 0 0 0 -1

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.103 0.116 0.029 0.000 0.000 0.000 0.000 0.000

Problem 248

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F(-2) F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 117 0 0 0 0 0 -1

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.109 0.120 0.028 0.000 0.000 0.000 0.000 0.000

Problem 249

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 113 0 0 0 0 0 -1

N.S.

1 1.00 1.02 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.108 0.065 0.055 0.000 0.000 0.000 0.000 0.000

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