Chapter 2
detailed summary tables of results

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 36, 37, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 183, 184, 186, 188, 189, 190, 191, 193, 194, 195, 196, 197, 198, 200, 201, 202, 206, 207, 208, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 227, 229, 230, 231, 232, 233, 235, 236, 237, 239, 240, 241, 242, 243, 244, 251, 252, 254, 255, 256, 257, 258, 259, 261, 262, 263, 264, 265, 266, 267, 268, 269, 272, 273, 274, 276, 277, 278, 279, 280, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 305, 309, 310, 311, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 325, 326, 328, 332, 333, 334, 335, 336, 340, 342, 343, 344, 348 }

B grade: { 28, 29, 34, 35, 52, 59, 181, 182, 185, 187, 192, 199, 203, 204, 205, 209, 210, 211, 226, 228, 234, 238, 245, 246, 247, 248, 249, 250, 253, 260, 270, 271, 275, 281, 282, 283, 300, 301, 302, 303, 304, 306, 307, 308, 312, 323, 324, 327, 329, 330, 331, 337, 338, 339, 341, 345, 346, 347 }

C grade: { 38, 39, 40, 41, 42, 43, 44, 60, 61, 62, 63, 64, 68, 132, 133 }

F grade: { }

2.1.3 Maple

A grade: { 4, 5, 6, 7, 12, 13, 14, 15, 19, 20, 21, 22, 26, 27, 30, 31, 32, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 71, 75, 76, 98, 99, 100, 104, 105, 106, 110, 111, 115, 116, 120, 121, 137, 138, 142, 143, 144, 145, 149, 150, 154, 155, 156, 160, 161, 162, 166, 167, 171, 172, 173, 177, 178, 182, 183, 184, 188, 189, 190, 192, 195, 196, 200, 201, 202, 206, 207, 208, 212, 213, 214, 215, 216, 217, 218, 219, 223, 227, 235, 239, 240, 241, 242, 243, 244, 245, 248, 254, 255, 256, 259, 261, 262, 265, 266, 267, 268, 272, 273, 274, 276, 278, 279, 280, 284, 285, 286, 290, 291, 292, 293, 297, 305, 309, 313, 314, 315, 316, 317, 318, 328, 332, 340, 348 }

B grade: { 1, 2, 3, 8, 9, 10, 11, 16, 17, 18, 23, 24, 25, 28, 29, 33, 34, 35, 95, 96, 97, 101, 102, 103, 107, 108, 109, 112, 113, 114, 117, 118, 119, 151, 152, 153, 157, 158, 159, 165, 170, 179, 180, 181, 185, 186, 187, 191, 193, 194, 197, 198, 199, 203, 204, 205, 209, 210, 211, 222, 226, 230, 231, 234, 238, 251, 252, 253, 257, 258, 260, 263, 264, 269, 270, 271, 275, 277, 281, 282, 283, 296, 300, 301, 304, 308, 312, 320, 323, 327, 331, 335, 336, 339, 343, 344, 347 }

C grade: { 77, 78, 79, 80, 81, 82, 83, 122, 123, 124, 319, 322 }

F grade: { 67, 68, 69, 70, 72, 73, 74, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 139, 140, 141, 146, 147, 148, 163, 164, 168, 169, 174, 175, 176, 220, 221, 224, 225, 228, 229, 232, 233, 236, 237, 246, 247, 249, 250, 287, 288, 289, 294, 295, 298, 299, 302, 303, 306, 307, 310, 311, 321, 324, 325, 326, 329, 330, 333, 334, 337, 338, 341, 342, 345, 346 }

2.1.4 Maxima

A grade: { 4, 19, 26, 27, 31, 36, 37, 65, 66, 71, 75, 76, 103, 115, 116, 137, 138, 142, 143, 144, 145, 149, 150, 159, 166, 167, 171, 172, 173, 177, 178, 182, 200, 215, 216, 217, 218, 219, 240, 241, 242, 243, 244, 253, 254, 255, 256, 264, 265, 266, 272, 273, 274, 279, 284, 290, 291, 297, 305, 309, 314, 315, 316, 317, 318, 332, 340, 348 }

B grade: { 1, 2, 3, 8, 9, 10, 11, 16, 17, 18, 23, 24, 25, 28, 29, 30, 33, 34, 35, 95, 96, 97, 101, 102, 107, 108, 109, 112, 113, 114, 117, 118, 119, 151, 152, 153, 157, 158, 179, 180, 181, 185, 186, 187, 188, 194, 197, 198, 199, 203, 204, 205, 206, 210, 211, 212, 251, 252, 257, 258, 259, 260, 263, 269, 270, 271, 275, 276, 277, 278, 281, 282, 283 }

C grade: { 5, 6, 7, 12, 13, 14, 15, 20, 21, 22, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 98, 99, 100, 104, 105, 106, 154, 155, 156, 160, 161, 162, 261, 262, 267, 268 }

F grade: { 32, 67, 68, 69, 70, 72, 73, 74, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 110, 111, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 139, 140, 141, 146, 147, 148, 163, 164, 165, 168, 169, 170, 174, 175, 176, 183, 184, 189, 190, 191, 192, 193, 195, 196, 201, 202, 207, 208, 209, 213, 214, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 245, 246, 247, 248, 249, 250, 280, 285, 286, 287, 288, 289, 292, 293, 294, 295, 296, 298, 299, 300, 301, 302, 303, 304, 306, 307, 308, 310, 311, 312, 313, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 333, 334, 335, 336, 337, 338, 339, 341, 342, 343, 344, 345, 346, 347 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 21, 26, 27, 30, 31, 32, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 110, 111, 114, 115, 116, 120, 121, 137, 138, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 166, 167, 171, 172, 173, 174, 175, 176, 177, 178, 182, 183, 184, 188, 189, 190, 193, 194, 195, 196, 201, 202, 207, 208, 213, 214, 215, 216, 217, 218, 219, 223, 227, 231, 235, 240, 241, 242, 243, 244, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 272, 273, 274, 277, 278, 279, 280, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 297, 301, 305, 309, 313, 314, 315, 316, 317, 318, 319, 328, 332, 336, 340, 344, 348 }

B grade: { 7, 14, 15, 22, 25, 29, 35, 52, 106, 108, 109, 113, 118, 119, 165, 170, 180, 181, 186, 187, 192, 199, 200, 205, 206, 211, 212, 222, 226, 230, 234, 238, 239, 245, 248, 253, 271, 276, 283, 296, 300, 304, 308, 312, 320, 322, 323, 327, 331, 335, 339, 343, 347 }

C grade: { 23, 24, 28, 33, 34, 107, 112, 117, 163, 164, 168, 169, 179, 185, 191, 197, 198, 203, 204, 209, 210, 220, 221, 224, 225, 228, 229, 232, 233, 236, 237, 246, 247, 249, 250, 251, 252, 269, 270, 275, 281, 282, 294, 295, 298, 299, 302, 303, 306, 307, 310, 311, 321, 324, 325, 326, 329, 330, 333, 334, 337, 338, 341, 342, 345, 346 }

F grade: { 67, 68, 70, 91, 92, 93, 94, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 139, 140, 141, 144 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 8, 9, 10, 11, 16, 17, 18, 19, 26, 27, 31, 32, 36, 37, 60, 61, 62, 63, 64, 65, 66, 71, 75, 76, 95, 96, 97, 101, 102, 103, 109, 110, 111, 114, 115, 116, 119, 120, 121, 137, 138, 142, 143, 144, 149, 150, 151, 152, 153, 157, 158, 159, 166, 177, 178, 181, 182, 183, 184, 187, 188, 189, 190, 193, 194, 201, 202, 207, 208, 213, 214, 215, 216, 217, 218, 219, 223, 240, 241, 242, 243, 244, 254, 255, 256, 257, 258, 259, 260, 263, 264, 265, 266, 273, 274, 279, 280, 285, 286, 290, 291, 292, 293, 297, 314, 315, 316, 317, 318 }

B grade: { }

C grade: { }

F grade: { 5, 6, 7, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 28, 29, 30, 33, 34, 35, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 67, 68, 69, 70, 72, 73, 74, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 98, 99, 100, 104, 105, 106, 107, 108, 112, 113, 117, 118, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 139, 140, 141, 145, 146, 147, 148, 154, 155, 156, 160, 161, 162, 163, 164, 165, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 179, 180, 185, 186, 191, 192, 195, 196, 197, 198, 199, 200, 203, 204, 205, 206, 209, 210, 211, 212, 220, 221, 222, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 245, 246, 247, 248, 249, 250, 251, 252, 253, 261, 262, 267, 268, 269, 270, 271, 272, 275, 276, 277, 278, 281, 282, 283, 284, 287, 288, 289, 294, 295, 296, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 8, 9, 10, 11, 16, 17, 18, 19, 26, 27, 31, 32, 36, 65, 66, 71, 75, 76, 95, 96, 97, 101, 102, 103, 110, 111, 115, 116, 120, 121, 122, 123, 124, 137, 138, 142, 143, 144, 145, 149, 150, 151, 152, 153, 157, 158, 159, 166, 167, 171, 173, 177, 178, 182, 183, 184, 188, 189, 190, 194, 195, 196, 200, 201, 206, 212, 215, 216, 217, 218, 219, 223, 227, 231, 235, 239, 240, 241, 242, 243, 244, 254, 255, 256, 260, 266, 272, 273, 274, 278, 279, 284, 290, 291, 292, 293, 297, 301, 305, 309, 313, 314, 315, 316, 317, 318, 328, 332, 336, 340, 348 }

B grade: { 6, 13, 21, 30, 99, 105, 109, 114, 119, 155, 161, 181, 277, 344 }

C grade: { 5, 7, 12, 14, 15, 20, 38, 39, 40, 41, 45, 46, 47, 48, 53, 54, 55, 56, 60, 61, 62, 98, 100, 104, 125, 126, 127, 154, 156, 160, 261, 262, 267 }

F grade: { 22, 23, 24, 25, 28, 29, 33, 34, 35, 37, 42, 43, 44, 49, 50, 51, 52, 57, 58, 59, 63, 64, 67, 68, 69, 70, 72, 73, 74, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 106, 107, 108, 112, 113, 117, 118, 128, 129, 130, 131, 132, 133, 134, 135, 136, 139, 140, 141, 146, 147, 148, 162, 163, 164, 165, 168, 169, 170, 172, 174, 175, 176, 179, 180, 185, 186, 187, 191, 192, 193, 197, 198, 199, 202, 203, 204, 205, 207, 208, 209, 210, 211, 213, 214, 220, 221, 222, 224, 225, 226, 228, 229, 230, 232, 233, 234, 236, 237, 238, 245, 246, 247, 248, 249, 250, 251, 252, 253, 257, 258, 259, 263, 264, 265, 268, 269, 270, 271, 275, 276, 280, 281, 282, 283, 285, 286, 287, 288, 289, 294, 295, 296, 298, 299, 300, 302, 303, 304, 306, 307, 308, 310, 311, 312, 319, 320, 321, 322, 323, 324, 325, 326, 327, 329, 330, 331, 333, 334, 335, 337, 338, 339, 341, 342, 343, 345, 346, 347 }

2.1.8 Mupad

A grade: { 26, 27, 31, 32, 36, 37, 65, 66, 71, 75, 76, 110, 111, 115, 116, 120, 121, 137, 138, 142, 143, 144, 145, 149, 150, 166, 167, 171, 172, 173, 177, 178, 183, 184, 189, 190, 195, 196, 201, 202, 207, 208, 213, 214, 215, 216, 217, 218, 219, 240, 241, 242, 243, 244, 255, 256, 273, 274, 279, 280, 285, 286, 290, 291, 292, 293, 314, 315, 316, 317, 318 }

B grade: { 1, 2, 3, 4, 8, 9, 10, 11, 16, 17, 18, 19, 30, 67, 69, 70, 95, 96, 97, 101, 102, 103, 109, 114, 119, 122, 123, 124, 151, 152, 153, 157, 158, 159, 181, 182, 187, 188, 193, 194, 200, 206, 212, 223, 227, 231, 235, 239, 254, 257, 258, 259, 260, 263, 264, 265, 266, 272, 277, 278, 284, 297, 301, 305, 309, 313, 328, 332, 336, 340, 344, 348 }

C grade: { }

F grade: { 5, 6, 7, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 28, 29, 33, 34, 35, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 68, 72, 73, 74, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 98, 99, 100, 104, 105, 106, 107, 108, 112, 113, 117, 118, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 139, 140, 141, 146, 147, 148, 154, 155, 156, 160, 161, 162, 163, 164, 165, 168, 169, 170, 174, 175, 176, 179, 180, 185, 186, 191, 192, 197, 198, 199, 203, 204, 205, 209, 210, 211, 220, 221, 222, 224, 225, 226, 228, 229, 230, 232, 233, 234, 236, 237, 238, 245, 246, 247, 248, 249, 250, 251, 252, 253, 261, 262, 267, 268, 269, 270, 271, 275, 276, 281, 282, 283, 287, 288, 289, 294, 295, 296, 298, 299, 300, 302, 303, 304, 306, 307, 308, 310, 311, 312, 319, 320, 321, 322, 323, 324, 325, 326, 327, 329, 330, 331, 333, 334, 335, 337, 338, 339, 341, 342, 343, 345, 346, 347 }

2.2 Detailed conclusion table per each integral for all CAS systems

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 normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\)