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Integrals 901 to 950

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 901

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

43 43 37 38 37 41 44 39 37

N.S.

1 1.00 0.86 0.88 0.86 0.95 1.02 0.91 0.86

time (sec)

N/A 0.137 0.022 0.781 0.186 0.251 0.423 0.280 0.105

Problem 902

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 42 69 44 79 41 52 71

N.S.

1 1.00 1.00 1.64 1.05 1.88 0.98 1.24 1.69

time (sec)

N/A 0.046 0.004 0.292 0.201 0.270 0.051 0.276 27.178

Problem 903

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 74 63 55 91 82 0 72 41

N.S.

1 1.00 0.85 0.74 1.23 1.11 0.00 0.97 0.55

time (sec)

N/A 0.274 0.084 0.422 0.275 0.249 0.000 0.324 27.273

Problem 904

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 47 32 176 39 17 949 34

N.S.

1 1.00 3.36 2.29 12.57 2.79 1.21 67.79 2.43

time (sec)

N/A 0.013 0.042 0.294 0.279 0.243 0.851 0.449 26.920

Problem 905

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

14 14 14 13 12 10 12 12 10

N.S.

1 1.00 1.00 0.93 0.86 0.71 0.86 0.86 0.71

time (sec)

N/A 0.045 0.013 0.707 0.196 0.258 0.509 0.277 0.219

Problem 906

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 10 0 24 0 9 18

N.S.

1 1.00 1.00 0.91 0.00 2.18 0.00 0.82 1.64

time (sec)

N/A 0.059 0.017 0.792 0.000 0.293 0.000 0.288 27.114

Problem 907

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 32 33 19 32 32 34 33

N.S.

1 1.00 0.94 0.97 0.56 0.94 0.94 1.00 0.97

time (sec)

N/A 0.060 0.024 0.307 0.231 0.229 0.488 0.271 26.508

Problem 908

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

21 21 25 18 17 17 24 17 18

N.S.

1 1.00 1.19 0.86 0.81 0.81 1.14 0.81 0.86

time (sec)

N/A 0.035 0.035 0.365 0.197 0.259 0.249 0.288 0.089

Problem 909

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 99 55 60 51 66 189 58 69

N.S.

1 1.00 0.56 0.61 0.52 0.67 1.91 0.59 0.70

time (sec)

N/A 0.065 0.147 1.624 0.207 0.259 0.189 0.279 26.537

Problem 910

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 40 41 59 51 0 70 64

N.S.

1 1.00 1.08 1.11 1.59 1.38 0.00 1.89 1.73

time (sec)

N/A 0.113 0.229 0.857 0.280 0.258 0.000 0.313 26.130

Problem 911

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

57 57 49 42 41 73 90 41 45

N.S.

1 1.00 0.86 0.74 0.72 1.28 1.58 0.72 0.79

time (sec)

N/A 0.084 0.080 0.897 0.190 0.244 0.609 0.284 26.355

Problem 912

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B C B F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 243 68 96 0 85 0 0 51

N.S.

1 4.26 1.19 1.68 0.00 1.49 0.00 0.00 0.89

time (sec)

N/A 0.231 0.045 24.511 0.000 0.263 0.000 0.000 28.437

Problem 913

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

5 5 5 8 7 17 7 10 10

N.S.

1 1.00 1.00 1.60 1.40 3.40 1.40 2.00 2.00

time (sec)

N/A 0.026 0.002 1.298 0.199 0.236 1.143 0.294 26.478

Problem 914

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

11 0 11 15 11 11 0 0 11

N.S.

1 0.00 1.00 1.36 1.00 1.00 0.00 0.00 1.00

time (sec)

N/A 0.000 0.344 1.819 0.260 0.259 0.000 0.000 27.236

Problem 915

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B A F B B

verified

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

size

27 0 24 22 74 27 0 93 38

N.S.

1 0.00 0.89 0.81 2.74 1.00 0.00 3.44 1.41

time (sec)

N/A 0.000 0.168 3.518 0.282 0.243 0.000 0.285 0.630

Problem 916

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

65 65 50 48 66 50 100 51 65

N.S.

1 1.00 0.77 0.74 1.02 0.77 1.54 0.78 1.00

time (sec)

N/A 0.080 0.055 2.255 0.205 0.236 0.182 0.270 26.115

Problem 917

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

8 8 8 17 10 14 0 0 10

N.S.

1 1.00 1.00 2.12 1.25 1.75 0.00 0.00 1.25

time (sec)

N/A 0.025 0.023 0.243 0.197 0.249 0.000 0.000 0.192

Problem 918

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F B A F F B

verified

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

size

32 32 32 0 125 41 0 0 45

N.S.

1 1.00 1.00 0.00 3.91 1.28 0.00 0.00 1.41

time (sec)

N/A 0.042 0.063 0.000 0.297 0.261 0.000 0.000 26.673

Problem 919

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

3 3 3 4 45 3 0 3 26

N.S.

1 1.00 1.00 1.33 15.00 1.00 0.00 1.00 8.67

time (sec)

N/A 0.034 0.014 0.651 0.217 0.263 0.000 0.265 27.038

Problem 920

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

35 35 32 31 35 27 39 27 34

N.S.

1 1.00 0.91 0.89 1.00 0.77 1.11 0.77 0.97

time (sec)

N/A 0.077 0.075 0.255 0.186 0.249 0.094 0.265 0.081

Problem 921

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

8 8 8 7 17 6 5 6 0

N.S.

1 1.00 1.00 0.88 2.12 0.75 0.62 0.75 0.00

time (sec)

N/A 0.009 0.004 0.286 0.227 0.249 0.343 0.268 0.000

Problem 922

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

37 37 29 30 0 29 0 29 0

N.S.

1 1.00 0.78 0.81 0.00 0.78 0.00 0.78 0.00

time (sec)

N/A 0.207 0.054 0.451 0.000 0.248 0.000 0.280 0.000

Problem 923

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

14 14 14 11 10 10 10 10 41

N.S.

1 1.00 1.00 0.79 0.71 0.71 0.71 0.71 2.93

time (sec)

N/A 0.014 0.005 0.226 0.183 0.239 5.247 0.307 27.747

Problem 924

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 10 9 8 20 7 8 19

N.S.

1 1.00 1.00 0.90 0.80 2.00 0.70 0.80 1.90

time (sec)

N/A 0.043 0.003 0.268 0.192 0.264 0.503 0.268 26.966

Problem 925

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

17 17 17 16 15 15 27 15 56

N.S.

1 1.00 1.00 0.94 0.88 0.88 1.59 0.88 3.29

time (sec)

N/A 0.026 0.015 0.551 0.191 0.246 1.227 0.271 26.987

Problem 926

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

129 129 120 127 126 85 241 155 147

N.S.

1 1.00 0.93 0.98 0.98 0.66 1.87 1.20 1.14

time (sec)

N/A 0.144 0.386 1.987 0.221 0.271 3.411 0.281 27.283

Problem 927

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B C B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 110 352 160 3830 115 0 1363 730

N.S.

1 1.00 3.20 1.45 34.82 1.05 0.00 12.39 6.64

time (sec)

N/A 0.126 0.795 52.376 0.458 0.279 0.000 0.845 43.077

Problem 928

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

6 6 6 7 36 12 0 20 14

N.S.

1 1.00 1.00 1.17 6.00 2.00 0.00 3.33 2.33

time (sec)

N/A 0.022 0.021 0.937 0.196 0.233 0.000 0.262 26.919

Problem 929

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

4 4 4 5 4 4 3 4 4

N.S.

1 1.00 1.00 1.25 1.00 1.00 0.75 1.00 1.00

time (sec)

N/A 0.011 0.001 0.144 0.202 0.246 0.095 0.265 27.682

Problem 930

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 30 24 98 39 22 908 23

N.S.

1 1.00 1.11 0.89 3.63 1.44 0.81 33.63 0.85

time (sec)

N/A 0.027 0.018 0.392 0.277 0.254 0.676 0.404 0.128

Problem 931

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 0 26 28 0 0 0 0 22

N.S.

1 0.00 1.00 1.08 0.00 0.00 0.00 0.00 0.85

time (sec)

N/A 0.000 0.362 1.366 0.000 0.000 0.000 0.000 28.340

Problem 932

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 26 28 24 26 0 26 26 26

N.S.

1 1.00 1.08 0.92 1.00 0.00 1.00 1.00 1.00

time (sec)

N/A 0.171 5.237 0.031 1.409 0.000 1.883 0.393 27.610

Problem 933

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A C B A A B B

verified

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

size

9 0 9 24 82 10 10 83 10

N.S.

1 0.00 1.00 2.67 9.11 1.11 1.11 9.22 1.11

time (sec)

N/A 0.000 0.356 1.288 0.333 0.249 0.146 0.268 26.757

Problem 934

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 76 60 57 60 150 62 111

N.S.

1 1.00 0.99 0.78 0.74 0.78 1.95 0.81 1.44

time (sec)

N/A 0.165 0.109 1.987 0.211 0.244 0.168 0.272 29.709

Problem 935

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 161 134 125 131 123 326 143 210

N.S.

1 1.00 0.83 0.78 0.81 0.76 2.02 0.89 1.30

time (sec)

N/A 0.335 0.308 2.758 0.199 0.257 0.496 0.305 30.876

Problem 936

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 89 105 70 79 72 201 70 73

N.S.

1 1.00 1.18 0.79 0.89 0.81 2.26 0.79 0.82

time (sec)

N/A 0.128 0.144 1.893 0.192 0.250 0.175 0.260 27.213

Problem 937

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

288 288 167 182 218 162 541 186 456

N.S.

1 1.00 0.58 0.63 0.76 0.56 1.88 0.65 1.58

time (sec)

N/A 0.511 1.658 3.716 0.221 0.252 0.546 0.311 28.969

Problem 938

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 61 55 132 0 108 0 0 51

N.S.

1 1.00 0.90 2.16 0.00 1.77 0.00 0.00 0.84

time (sec)

N/A 0.344 0.606 1.421 0.000 0.096 0.000 0.000 27.982

Problem 939

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

148 148 137 256 0 210 0 0 129

N.S.

1 1.00 0.93 1.73 0.00 1.42 0.00 0.00 0.87

time (sec)

N/A 0.311 1.129 2.597 0.000 0.107 0.000 0.000 31.509

Problem 940

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 43 32 50 30 73 31 35

N.S.

1 1.00 1.26 0.94 1.47 0.88 2.15 0.91 1.03

time (sec)

N/A 0.119 0.075 0.736 0.208 0.257 0.484 0.345 27.673

Problem 941

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 43 34 62 30 71 31 35

N.S.

1 1.00 1.19 0.94 1.72 0.83 1.97 0.86 0.97

time (sec)

N/A 0.119 0.121 0.763 0.212 0.256 0.509 0.367 27.052

Problem 942

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 120 73 111 0 150 379 128 226

N.S.

1 1.00 0.61 0.92 0.00 1.25 3.16 1.07 1.88

time (sec)

N/A 0.876 8.946 1.424 0.000 0.277 84.523 0.481 28.342

Problem 943

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 25 72 58 74 122 48 23

N.S.

1 1.00 0.35 1.00 0.81 1.03 1.69 0.67 0.32

time (sec)

N/A 0.200 0.029 1.046 0.319 0.277 1.716 0.350 25.950

Problem 944

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 55 42 51 154 42 76 52 105

N.S.

1 1.00 0.76 0.93 2.80 0.76 1.38 0.95 1.91

time (sec)

N/A 0.516 10.011 1.220 0.310 0.254 0.423 0.354 27.042

Problem 945

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 33 15 22 16 32 14 14

N.S.

1 1.00 2.06 0.94 1.38 1.00 2.00 0.88 0.88

time (sec)

N/A 0.070 0.011 0.625 0.222 0.246 0.118 0.296 26.985

Problem 946

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 19 18 22 31 29 50

N.S.

1 1.00 1.00 1.06 1.00 1.22 1.72 1.61 2.78

time (sec)

N/A 0.032 0.186 0.623 0.187 0.249 0.208 0.287 27.438

Problem 947

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 19 30 70 22 0 29 50

N.S.

1 1.00 1.00 1.58 3.68 1.16 0.00 1.53 2.63

time (sec)

N/A 0.368 0.414 1.007 0.289 0.243 0.000 0.317 27.567

Problem 948

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 33 15 23 17 0 14 14

N.S.

1 1.00 1.94 0.88 1.35 1.00 0.00 0.82 0.82

time (sec)

N/A 0.206 0.010 0.737 0.204 0.236 0.000 0.313 26.226

Problem 949

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 54 42 51 154 42 0 52 106

N.S.

1 1.00 0.78 0.94 2.85 0.78 0.00 0.96 1.96

time (sec)

N/A 0.620 11.061 1.291 0.287 0.266 0.000 0.381 26.948

Problem 950

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 26 72 58 74 0 48 23

N.S.

1 1.00 0.36 1.00 0.81 1.03 0.00 0.67 0.32

time (sec)

N/A 1.591 0.022 1.020 0.283 0.261 0.000 0.389 26.874

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