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, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361 }

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, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 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, 292, 293, 294, 295, 297, 298, 299, 300, 301, 302, 303, 304, 306, 307, 308, 309, 311, 313, 314, 315, 316, 317, 318, 320, 321, 322, 324, 325, 326, 328, 330, 331, 332, 333, 334, 335, 337, 338, 339, 341, 342, 343, 345, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360 }

B grade: { 47, 57, 71, 78, 84, 291, 296, 305, 310, 312, 319, 323, 327, 329, 336, 340, 344, 346 }

C grade: { 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 361 }

F grade: { }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 13, 14, 15, 28, 30, 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, 72, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 88, 89, 90, 91, 92, 97, 98, 99, 100, 101, 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, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 152, 153, 154, 155, 156, 157, 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, 195, 196, 197, 198, 202, 203, 204, 205, 206, 209, 210, 211, 212, 213, 214, 217, 219, 220, 221, 222, 228, 229, 230, 231, 237, 238, 239, 240, 243, 244, 245, 246, 247, 248, 251, 252, 253, 254, 255, 256, 259, 261, 262, 263, 264, 270, 275, 276, 277, 278, 279, 280, 281, 287, 292, 297, 301, 306, 311, 316, 320, 324, 328, 333, 337, 341, 345, 346, 347, 348, 352, 357 }

B grade: { 9, 10, 11, 12, 29, 31, 32, 71, 78, 84, 86, 87, 94, 95, 96, 103, 104, 105, 134, 149, 150, 151, 158, 159, 191, 192, 193, 194, 199, 200, 201, 207, 208, 215, 216, 218, 223, 224, 225, 226, 227, 232, 233, 234, 235, 236, 241, 242, 249, 250, 257, 258, 260, 266, 267, 268, 269, 286, 291, 296, 300, 305, 310, 315, 319, 323, 327, 332, 336, 340, 344, 349, 350, 351, 353, 354 }

C grade: { 274, 282, 283, 284, 285, 288, 289, 290, 293, 294, 295, 298, 299, 302, 303, 304, 307, 308, 309, 312, 313, 314, 317, 318, 321, 322, 325, 326, 329, 330, 331, 334, 335, 338, 339, 342, 343, 355, 356, 358, 359, 360, 361 }

F grade: { 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 85, 93, 102, 265, 271, 272, 273 }

2.1.4 Maxima

A grade: { 5, 6, 7, 8, 9, 10, 11, 28, 29, 30, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 120, 121, 122, 123, 124, 129, 130, 131, 132, 133, 140, 141, 142, 143, 144, 149, 150, 151, 152, 153, 158, 159, 160, 161, 162, 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, 218, 219, 220, 221, 222, 228, 229, 230, 231, 237, 238, 239, 240, 245, 246, 247, 248, 254, 255, 256, 262, 263, 264, 266, 267, 268, 269, 270, 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, 316, 320, 324, 328, 333, 337, 341, 345, 348, 350, 351, 352, 353, 354, 356, 357, 358, 359 }

B grade: { 12, 48, 58, 71, 72, 78, 84, 315, 319, 321, 322, 323, 325, 326, 327, 332, 336, 338, 339, 340, 342, 343, 344, 346, 347, 349, 355, 360 }

C grade: { }

F grade: { 1, 2, 3, 4, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 31, 32, 33, 54, 85, 93, 102, 116, 117, 118, 119, 125, 126, 127, 128, 134, 135, 136, 137, 138, 139, 145, 146, 147, 148, 154, 155, 156, 157, 163, 164, 165, 166, 215, 216, 217, 223, 224, 225, 226, 227, 232, 233, 234, 235, 236, 241, 242, 243, 244, 249, 250, 251, 252, 253, 257, 258, 259, 260, 261, 265, 271, 272, 273, 312, 313, 314, 317, 318, 329, 330, 331, 334, 335, 361 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 28, 30, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 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, 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, 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, 269, 270, 274, 275, 276, 277, 278, 279, 280, 287, 292, 297, 301, 306, 311, 316, 320, 324, 328, 333, 337, 340, 341, 344, 345, 352, 356, 357, 358, 359 }

B grade: { 13, 14, 15, 29, 44, 54, 58, 65, 72, 84, 133, 162, 266, 267, 268, 281, 286, 291, 296, 300, 305, 310, 315, 319, 323, 327, 332, 336, 346, 349, 355, 360 }

C grade: { 282, 283, 284, 285, 288, 289, 290, 293, 294, 295, 298, 299, 302, 303, 304, 307, 308, 309, 312, 313, 314, 317, 318, 321, 322, 325, 326, 329, 330, 331, 334, 335, 338, 339, 342, 343, 347, 348, 350, 351, 353, 354, 361 }

F grade: { 4, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 31, 32, 33, 85, 93, 102, 265, 271, 272, 273 }

2.1.6 Sympy

A grade: { 1, 2, 3, 9, 10, 11, 12, 28, 30, 34, 35, 37, 38, 39, 41, 42, 43, 45, 46, 47, 48, 51, 52, 53, 55, 56, 57, 58, 62, 64, 66, 67, 68, 69, 70, 71, 72, 77, 79, 80, 81, 82, 83, 84, 115, 123, 124, 169, 172, 173, 174, 181, 182, 189, 190, 270, 275, 276, 277, 279, 280, 287, 292, 297, 301, 306, 311, 316, 320, 324, 328, 333, 337, 341, 345, 357 }

B grade: { 63, 78 }

C grade: { }

F grade: { 4, 5, 6, 7, 8, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 31, 32, 33, 36, 40, 44, 49, 50, 54, 59, 60, 61, 65, 73, 74, 75, 76, 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, 116, 117, 118, 119, 120, 121, 122, 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, 170, 171, 175, 176, 177, 178, 179, 180, 183, 184, 185, 186, 187, 188, 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, 271, 272, 273, 274, 278, 281, 282, 283, 284, 285, 286, 288, 289, 290, 291, 293, 294, 295, 296, 298, 299, 300, 302, 303, 304, 305, 307, 308, 309, 310, 312, 313, 314, 315, 317, 318, 319, 321, 322, 323, 325, 326, 327, 329, 330, 331, 332, 334, 335, 336, 338, 339, 340, 342, 343, 344, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 358, 359, 360, 361 }

2.1.7 Giac

A grade: { 5, 6, 7, 8, 24, 30, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 115, 116, 117, 118, 119, 125, 126, 127, 128, 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, 220, 221, 222, 223, 224, 228, 229, 230, 231, 232, 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, 267, 268, 269, 270, 287, 292, 297, 301, 306, 311, 316, 320, 324, 328, 333, 337, 341, 345, 355, 357, 358, 360 }

B grade: { 28, 29, 58, 72, 84, 113, 114, 120, 121, 122, 123, 124, 129, 130, 131, 132, 133, 219, 266, 275, 276, 277, 279, 280, 356, 359 }

C grade: { 278 }

F grade: { 1, 2, 3, 4, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 31, 32, 33, 44, 54, 65, 85, 93, 102, 225, 226, 227, 233, 234, 235, 236, 265, 271, 272, 273, 274, 281, 282, 283, 284, 285, 286, 288, 289, 290, 291, 293, 294, 295, 296, 298, 299, 300, 302, 303, 304, 305, 307, 308, 309, 310, 312, 313, 314, 315, 317, 318, 319, 321, 322, 323, 325, 326, 327, 329, 330, 331, 332, 334, 335, 336, 338, 339, 340, 342, 343, 344, 346, 347, 348, 349, 350, 351, 352, 353, 354, 361 }

2.1.8 Mupad

A grade: { 30, 34, 35, 287, 292, 297, 301, 306, 311, 316, 320, 324, 328, 333, 337, 341, 345 }

B grade: { 12, 28, 29, 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, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 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, 219, 220, 221, 222, 228, 229, 230, 231, 237, 238, 239, 240, 245, 246, 247, 248, 253, 254, 255, 256, 260, 261, 262, 263, 264, 266, 267, 268, 269, 270, 274, 275, 276, 277, 278, 279, 280, 355, 356, 357, 358, 359, 360 }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 31, 32, 33, 85, 93, 102, 215, 216, 217, 218, 223, 224, 225, 226, 227, 232, 233, 234, 235, 236, 241, 242, 243, 244, 249, 250, 251, 252, 257, 258, 259, 265, 271, 272, 273, 281, 282, 283, 284, 285, 286, 288, 289, 290, 291, 293, 294, 295, 296, 298, 299, 300, 302, 303, 304, 305, 307, 308, 309, 310, 312, 313, 314, 315, 317, 318, 319, 321, 322, 323, 325, 326, 327, 329, 330, 331, 332, 334, 335, 336, 338, 339, 340, 342, 343, 344, 346, 347, 348, 349, 350, 351, 352, 353, 354, 361 }

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 \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\)