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2.2.3 Integrals 201 to 249

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 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

40 40 51 0 0 0 0 0 0

N.S.

1 1.00 1.28 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.244 0.007 0.000 0.000 0.000 0.000 0.000 0.000

Problem 202

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

23 23 25 23 25 25 19 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.83 1.09 1.09

time (sec)

N/A 0.181 0.067 0.026 0.213 0.246 1.450 0.294 0.465

Problem 203

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

23 23 25 23 25 42 20 25 25

N.S.

1 1.00 1.09 1.00 1.09 1.83 0.87 1.09 1.09

time (sec)

N/A 0.267 0.035 0.029 0.214 0.251 2.910 0.301 0.489

Problem 204

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

23 23 25 23 25 59 20 25 25

N.S.

1 1.00 1.09 1.00 1.09 2.57 0.87 1.09 1.09

time (sec)

N/A 0.352 0.037 0.027 0.213 0.265 6.926 0.432 0.438

Problem 205

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 20 20 0 0 0 15 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.75 0.00 0.00

time (sec)

N/A 0.212 0.004 0.000 0.000 0.000 1.004 0.000 0.000

Problem 206

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

33 35 33 0 0 0 0 0 0

N.S.

1 1.06 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.264 0.004 0.000 0.000 0.000 0.000 0.000 0.000

Problem 207

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 26 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.246 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 208

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

217 280 196 269 0 247 250 0 0

N.S.

1 1.29 0.90 1.24 0.00 1.14 1.15 0.00 0.00

time (sec)

N/A 0.574 0.397 30.191 0.000 0.277 72.227 0.000 0.000

Problem 209

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

185 240 168 228 0 207 206 0 0

N.S.

1 1.30 0.91 1.23 0.00 1.12 1.11 0.00 0.00

time (sec)

N/A 0.510 0.252 12.649 0.000 0.287 22.171 0.000 0.000

Problem 210

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 129 113 169 0 137 136 0 0

N.S.

1 1.22 1.07 1.59 0.00 1.29 1.28 0.00 0.00

time (sec)

N/A 0.432 0.071 4.876 0.000 0.271 6.034 0.000 0.000

Problem 211

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 26 30 0 0 0 26 0 0

N.S.

1 1.00 1.15 0.00 0.00 0.00 1.00 0.00 0.00

time (sec)

N/A 0.229 0.005 0.000 0.000 0.000 6.946 0.000 0.000

Problem 212

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 166 115 204 0 134 0 0 0

N.S.

1 1.17 0.81 1.44 0.00 0.94 0.00 0.00 0.00

time (sec)

N/A 0.435 0.135 4.753 0.000 0.253 0.000 0.000 0.000

Problem 213

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

202 245 163 268 0 190 0 0 0

N.S.

1 1.21 0.81 1.33 0.00 0.94 0.00 0.00 0.00

time (sec)

N/A 0.535 0.151 4.711 0.000 0.265 0.000 0.000 0.000

Problem 214

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

253 402 0 0 0 296 0 0 0

N.S.

1 1.59 0.00 0.00 0.00 1.17 0.00 0.00 0.00

time (sec)

N/A 1.076 0.000 0.000 0.000 0.295 0.000 0.000 0.000

Problem 215

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

221 352 0 0 0 257 0 0 0

N.S.

1 1.59 0.00 0.00 0.00 1.16 0.00 0.00 0.00

time (sec)

N/A 0.950 0.000 0.000 0.000 0.279 0.000 0.000 0.000

Problem 216

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

131 189 0 0 0 172 0 0 0

N.S.

1 1.44 0.00 0.00 0.00 1.31 0.00 0.00 0.00

time (sec)

N/A 0.728 0.000 0.000 0.000 0.269 0.000 0.000 0.000

Problem 217

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 26 30 0 0 0 26 0 0

N.S.

1 1.00 1.15 0.00 0.00 0.00 1.00 0.00 0.00

time (sec)

N/A 0.228 0.006 0.000 0.000 0.000 3.781 0.000 0.000

Problem 218

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

174 237 0 0 0 156 0 0 0

N.S.

1 1.36 0.00 0.00 0.00 0.90 0.00 0.00 0.00

time (sec)

N/A 0.765 0.000 0.000 0.000 0.267 0.000 0.000 0.000

Problem 219

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

238 349 0 0 0 221 0 0 0

N.S.

1 1.47 0.00 0.00 0.00 0.93 0.00 0.00 0.00

time (sec)

N/A 1.001 0.000 0.000 0.000 0.278 0.000 0.000 0.000

Problem 220

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 26 266 844 172 43 0 28 28

N.S.

1 1.00 10.23 32.46 6.62 1.65 0.00 1.08 1.08

time (sec)

N/A 0.192 0.296 146.060 0.320 0.285 0.000 1.119 1.016

Problem 221

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

23 23 25 867 302 35 0 24 25

N.S.

1 1.00 1.09 37.70 13.13 1.52 0.00 1.04 1.09

time (sec)

N/A 0.435 0.096 0.089 0.292 0.316 0.000 0.336 0.606

Problem 222

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

23 23 25 1065 427 31 22 25 25

N.S.

1 1.00 1.09 46.30 18.57 1.35 0.96 1.09 1.09

time (sec)

N/A 0.966 0.059 2.004 0.323 0.355 11.254 0.317 0.590

Problem 223

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

27 27 27 24 23 32 22 32 23

N.S.

1 1.00 1.00 0.89 0.85 1.19 0.81 1.19 0.85

time (sec)

N/A 0.215 0.003 0.317 0.182 0.264 0.324 0.314 0.532

Problem 224

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

27 27 27 24 23 32 22 32 23

N.S.

1 1.00 1.00 0.89 0.85 1.19 0.81 1.19 0.85

time (sec)

N/A 0.196 0.002 0.086 0.184 0.279 0.202 0.355 0.504

Problem 225

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

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 0.183 0.002 0.066 0.186 0.294 0.121 0.355 0.027

Problem 226

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

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 0.204 0.002 0.112 0.176 0.273 0.553 0.322 0.534

Problem 227

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

23 23 23 20 23 20 17 25 19

N.S.

1 1.00 1.00 0.87 1.00 0.87 0.74 1.09 0.83

time (sec)

N/A 0.206 0.002 0.094 0.175 0.296 0.202 0.407 0.506

Problem 228

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

27 27 27 22 23 24 24 28 23

N.S.

1 1.00 1.00 0.81 0.85 0.89 0.89 1.04 0.85

time (sec)

N/A 0.205 0.002 0.155 0.181 0.274 0.395 0.300 0.553

Problem 229

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

27 27 27 22 23 24 24 28 23

N.S.

1 1.00 1.00 0.81 0.85 0.89 0.89 1.04 0.85

time (sec)

N/A 0.203 0.002 0.298 0.189 0.285 0.642 0.300 0.504

Problem 230

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 53 52 47 46 113 49 115 46

N.S.

1 1.02 1.00 0.90 0.88 2.17 0.94 2.21 0.88

time (sec)

N/A 0.270 0.004 0.290 0.175 0.296 0.575 0.294 0.547

Problem 231

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 51 43 47 46 113 46 112 46

N.S.

1 0.98 0.83 0.90 0.88 2.17 0.88 2.15 0.88

time (sec)

N/A 0.249 0.005 0.157 0.177 0.293 0.334 0.324 0.537

Problem 232

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 37 37 40 39 90 39 92 39

N.S.

1 0.95 0.95 1.03 1.00 2.31 1.00 2.36 1.00

time (sec)

N/A 0.224 0.003 0.090 0.183 0.292 0.189 0.301 0.540

Problem 233

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes 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 0.217 0.002 0.106 0.182 0.285 0.528 0.290 0.485

Problem 234

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

46 45 40 41 46 81 41 90 40

N.S.

1 0.98 0.87 0.89 1.00 1.76 0.89 1.96 0.87

time (sec)

N/A 0.264 0.004 0.095 0.188 0.283 0.201 0.313 0.546

Problem 235

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 50 43 42 46 87 48 94 46

N.S.

1 0.96 0.83 0.81 0.88 1.67 0.92 1.81 0.88

time (sec)

N/A 0.261 0.005 0.158 0.187 0.287 0.394 0.308 0.539

Problem 236

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 53 52 43 46 88 51 95 46

N.S.

1 1.02 1.00 0.83 0.88 1.69 0.98 1.83 0.88

time (sec)

N/A 0.257 0.003 0.300 0.207 0.277 0.614 0.303 0.547

Problem 237

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 137 91 677 282 1358 0 1857 0

N.S.

1 1.01 0.67 5.01 2.09 10.06 0.00 13.76 0.00

time (sec)

N/A 0.489 0.039 19.105 0.217 0.305 0.000 0.441 0.000

Problem 238

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 94 90 282 149 391 0 576 0

N.S.

1 1.01 0.97 3.03 1.60 4.20 0.00 6.19 0.00

time (sec)

N/A 0.353 0.027 2.997 0.209 0.285 0.000 0.504 0.000

Problem 239

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 51 37 82 62 72 109 114 0

N.S.

1 1.00 0.73 1.61 1.22 1.41 2.14 2.24 0.00

time (sec)

N/A 0.233 0.010 0.460 0.193 0.289 1.480 0.328 0.000

Problem 240

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

86 86 85 0 0 105 0 0 0

N.S.

1 1.00 0.99 0.00 0.00 1.22 0.00 0.00 0.00

time (sec)

N/A 0.415 0.135 0.000 0.000 0.289 0.000 0.000 0.000

Problem 241

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

127 127 112 0 0 202 0 0 0

N.S.

1 1.00 0.88 0.00 0.00 1.59 0.00 0.00 0.00

time (sec)

N/A 0.524 0.238 0.000 0.000 0.286 0.000 0.000 0.000

Problem 242

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

134 134 133 0 0 0 0 0 0

N.S.

1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.442 0.181 0.000 0.000 0.000 0.000 0.000 0.000

Problem 243

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

117 117 117 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.415 0.127 0.000 0.000 0.000 0.000 0.000 0.000

Problem 244

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

117 117 117 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.384 0.115 0.000 0.000 0.000 0.000 0.000 0.000

Problem 245

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

108 108 108 0 0 73 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.68 0.00 0.00 0.00

time (sec)

N/A 0.347 0.102 0.000 0.000 0.096 0.000 0.000 0.000

Problem 246

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

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 0.271 0.008 0.665 0.184 0.261 1.071 0.404 0.689

Problem 247

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

107 107 107 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.396 0.114 0.000 0.000 0.000 0.000 0.000 0.000

Problem 248

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

117 117 117 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.410 0.121 0.000 0.000 0.000 0.000 0.000 0.000

Problem 249

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

111 101 113 0 0 0 0 0 0

N.S.

1 0.91 1.02 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.429 0.070 0.000 0.000 0.000 0.000 0.000 0.000

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