axiom-developer
[Top][All Lists]
Advanced

[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

[Axiom-developer] Re: About Schaums.


From: root
Subject: [Axiom-developer] Re: About Schaums.
Date: Wed, 30 Apr 2008 14:58:05 -0400

How many integrals is there in the book ? ... 619 
How many do you test ? (all ?!) .... all
How many are immediately the same ? 
How many are false ? (no one I expect !) 
How many differs ?
Do you have any idea about the result of others CAS ? 
  .... no but this effort is called CATS (Computer Algebra Test Suite)
  and is intended to be tested against, and used as a standard for test
  against, other systems. I plan to test other systems as time permits.

All of these results can be found in the axiom distribution under
  src/input/schaum*.input.pamphlet

===============================================================
619 integrals
   237 agreements (differ by 0) (38%)
   134 differ by a constant (22%)
 371 total (60%)
   108 simplification failures (17.5%)
   135 integrals not in closed form (21.5%)
 243 total (39%)

There were a few "other" answers which were not part of the above. 
Of interest was:

  Axiom found 2 typos in Schaums (1968 printing 4)

  Differing by a constant seems to be related to the choice of 
  signs and branch cuts. There is much of interest to be learned
  by these values which I hope to explore later.

  Axiom has a closed form for 2 integrals where Schaums has series.

    Axiom claims to be a "decision procedure" for elementary integrals.
    If there is a closed form for the result, Axiom will return it.
    If Axiom returns the original integral, then no closed form exists.

  It is undecided if the values that did not simplify agree with Schaums.
  These simplifications will be checked in more detail using Axiom and
  other computer algebra systems. In particular, this has caused me to 
  work on a more general purpose simplification procedure for Axiom.

(Spiegel, Murray R.; Schaums Mathematical Handbook, 1968, printing 4)
(Axiom March 2008 release)

  14:59 Schaums and Axiom agree
  14:60 Schaums and Axiom agree
  14:61 Schaums and Axiom differ by a constant
  14:62 Schaums and Axiom differ by a constant
  14:63 Schaums and Axiom agree
  14:64 Schaums and Axiom agree
  14:65 Schaums and Axiom agree
  14:66 Schaums and Axiom agree
  14:67 Schaums and Axiom agree
  14:68 Schaums and Axiom differ by a constant
  14:69 Schaums and Axiom differ by a constant
  14:70 Schaums and Axiom agree
  14:71 Schaums and Axiom agree
  14:72 Schaums and Axiom differ by a constant
  14:73 Schaums and Axiom differ by a constant
  14:74 Schaums and Axiom agree
  14:75 Schaums and Axiom agree
  14:76 Schaums and Axiom agree
  14:77 Schaums and Axiom differ by a constant
  14:78 Schaums and Axiom agree
  14:79 Schaums and Axiom agree
  14:80 Schaums and Axiom agree
  14:82 Schaums and Axiom agree
  14:83 Axiom cannot do this integration
  14:84 Schaums and Axiom agree
  14:85 Schaums and Axiom agree
  14:86 Schaums and Axiom agree
  14:87a Schaums and Axiom differ by a constant
  14:87b Schaums and Axiom differ by a constant
  14:88 Schaums and Axiom differ by a constant
  14:89 Schaums and Axiom differ by a constant
  14:90 Schaums and Axiom agree
  14:91 Axiom cannot simplify this expression. Schaums typo?
  14:92 Axiom cannot simplify this expression
  14:93 Schaums and Axiom agree
  14:94 Axiom cannot do this integral
  14:95 Axiom cannot do this integral
  14:96 Axiom cannot do this integral
  14:97 Axiom cannot do this integral
  14:98 Axiom cannot do this integral
  14:99 Schaums and Axiom agree
  14:xxx Schaums and Axiom agree
  14:100 Schaums and Axiom agree
  14:101 Schaums and Axiom agree
  14:102 Axiom cannot do this integral
  14:103 Axiom cannot do this integral
  14:104 Axiom cannot do this integral
  14:105 Schaums and Axiom agree
  14:106 Schaums and Axiom agree
  14:107 Schaums and Axiom agree
  14:108 Schaums and Axiom agree
  14:109 Schaums and Axiom agree
  14:110 Axiom cannot do this integral
  14:111 Schaums and Axiom agree
  14:112 Axiom cannot do this integral
  14:113 Schaums and Axiom agree
  14:114 Axiom cannot simplify these answers
  14:115 Axiom cannot simplify these answers
  14:116 Axiom cannot compute this integral
  14:117 Axiom cannot compute this integral
  14:118 Axiom cannot compute this integral
  14:119 Axiom cannot compute this integral
  14:120 Axiom cannot simplify these answers
  14:121 Axiom cannot simplify this answer
  14:122 Axiom cannot simplify this answer
  14:123 Axiom cannot simplify these results
  14:124 Axiom cannot simplify this result
  14:125 Schaums and Axiom agree
  14:126 Schaums and Axiom agree
  14:127 Schaums and Axiom agree
  14:128 Schaums and Axiom agree
  14:129 Schaums and Axiom agree
  14:130 Schaums and Axiom agree
  14:131 Schaums and Axiom agree
  14:132 Schaums and Axiom agree
  14:133 Schaums and Axiom agree
  14:134 Schaums and Axiom agree
  14:135 Schaums and Axiom agree
  14:136 Schaums and Axiom agree
  14:137 Schaums and Axiom agree
  14:138 Schaums and Axiom agree
  14:139 Axiom cannot do this integral
  14:140 Schaums and Axiom agree
  14:141 Axiom cannot do this integral
  14:142 Axiom cannot do this integral
  14:143 Axiom cannot do this integral
  14:144 Schaums and Axiom agree
  14:145 Schaums and Axiom agree
  14:146 Schaums and Axiom agree
  14:147 Schaums and Axiom agree
  14:148 Schaums and Axiom agree
  14:149 Schaums and Axiom agree
  14:150 Schaums and Axiom agree
  14:151 Schaums and Axiom agree
  14:152 Schaums and Axiom agree
  14:153 Schaums and Axiom agree
  14:154 Schaums and Axiom agree
  14:155 Schaums and Axiom agree
  14:156 Schaums and Axiom agree
  14:157 Schaums and Axiom agree
  14:158 Axiom cannot do this integral
  14:159 Schaums and Axiom agree
  14:160 Axiom cannot compute this integral
  14:161 Axiom cannot compute this integral
  14:162 Axiom cannot compute this integral
  14:163 Schaums and Axiom differ by a constant
  14:164 Schaums and Axiom differ by a constant
  14:165 Schaums and Axiom differ by a constant
  14:166 Schaums and Axiom differ by a constant
  14:167 Schaums and Axiom differ by a constant
  14:168 Schaums and Axiom differ by a constant
  14:169 Schaums and Axiom differ by a constant
  14:170 Schaums and Axiom differ by a constant
  14:171 Schaums and Axiom agree
  14:172 Schaums and Axiom differ by a constant
  14:173 Schaums and Axiom differ by a constant
  14:174 Schaums and Axiom differ by a constant
  14:175 Schaums and Axiom differ by a constant
  14:176 Schaums and Axiom differ by a constant
  14:177 Axiom cannot do this integration
  14:178 Schaums and Axiom agree
  14:179 Axiom cannot integrate this expression
  14:180 Axiom cannot integrate this expression
  14:181 Axiom cannot integrate this expression
  14:182 Schaums and Axiom differ by a constant
  14:183 Schaums and Axiom agree
  14:184 Schaums and Axiom differ by a constant
  14:185 Schaums and Axiom agree
  14:186 Schaums and Axiom differ by a constant
  14:187 Schaums and Axiom differ by a constant
  14:188 Schaums and Axiom differ by a constant
  14:189 Schaums and Axiom differ by a constant
  14:190 Schaums and Axiom agree
  14:191 Schaums and Axiom differ by a constant
  14:192 Schaums and Axiom agree
  14:193 Schaums and Axiom differ by a constant
  14:194 Schaums and Axiom differ by a constant
  14:195 Schaums and Axiom differ by a constant
  14:196 Schaums and Axiom differ by a constant
  14:197 Schaums and Axiom agree
  14:198 Schaums and Axiom differ by a constant
  14:199 Schaums and Axiom agree
  14:200 Schaums and Axiom differ by a constant
  14:201 Schaums and Axiom differ by a constant
  14:202 Schaums and Axiom differ by a constant
  14:203 Schaums and Axiom differ by a constant
  14:204 Schaums and Axiom agree
  14:205 Schaums and Axiom differ by a constant
  14:206 Schaums and Axiom agree
  14:207 Schaums and Axiom differ by a constant
  14:208 Schaums and Axiom differ by a constant
  14:209 Schaums and Axiom differ by a constant
  14:210 Schaums and Axiom differ by a constant
  14:211 Schaums and Axiom differ by a constant
  14:212 Schaums and Axiom agree
  14:213 Schaums and Axiom differ by a constant
  14:214 Schaums and Axiom differ by a constant
  14:215 Schaums and Axiom differ by a constant
  14:216 Schaums and Axiom differ by a constant 
  14:217 Schaums and Axiom agree
  14:218 Schaums and Axiom differ by a constant
  14:219 Schaums and Axiom agree
  14:220 Schaums and Axiom differ by a constant
  14:221 Schaums and Axiom differ by a constant
  14:222 Schaums and Axiom differ by a constant
  14:223 Schaums and Axiom differ by a constant
  14:224 Schaums and Axiom agree
  14:225 Schaums and Axiom differ by a constant
  14:226 Schaums and Axiom agree
  14:227 Schaums and Axiom differ by a constant
  14:228 Schaums and Axiom differ by a constant
  14:229 Schaums and Axiom differ by a constant
  14:230 Schaums and Axiom differ by a constant
  14:231 Schaums and Axiom agree
  14:232 Schaums and Axiom differ by a constant
  14:233 Schaums and Axiom agree
  14:234 Schaums and Axiom differ by a constant
  14:235 Schaums and Axiom differ by a constant
  14:236 Schaums and Axiom differ by a constant
  14:238 Schaums and Axiom agree
  14:238 Schaums and Axiom differ by a constant
  14:239 Schaums and Axiom agree
  14:240 Schaums and Axiom differ by a constant
  14:241 Schaums and Axiom differ by a constant
  14:242 Schaums and Axiom agree
  14:243 Schaums and Axiom differ by a constant
  14:244 Schaums and Axiom agree
  14:245 Schaums and Axiom differ by a constant
  14:246 Schaums and Axiom agree
  14:247 Schaums and Axiom differ by a constant
  14:248 Schaums and Axiom differ by a constant
  14:249 Schaums and Axiom agree
  14:250 Schaums and Axiom differ by a constant
  14:251 Schaums and Axiom agree
  14:252 Schaums and Axiom differ by a constant
  14:253 Schaums and Axiom agree
  14:254 Schaums and Axiom differ by a constant
  14:255 Schaums and Axiom differ by a constant
  14:256 Schaums and Axiom agree
  14:257 Schaums and Axiom differ by a constant
  14:258 Schaums and Axiom agree
  14:259 Schaums and Axiom differ by a constant
  14:260 Schaums and Axiom agree
  14:261 Schaums and Axiom differ by a constant
  14:262 Schaums and Axiom differ by a constant
  14:263 Schaums and Axiom agree
  14:264 Schaums and Axiom differ by a constant
  14:265 Axiom cannot simplify these expressions
  14:266 Axiom cannot simplify these expressions
  14:267 Schaums and Axiom differ by a constant
  14:268 Axiom cannot compute this integral
  14:269 Schaums and Axiom differ by a constant
  14:270 Schaums and Axiom differ by a constant
  14:271 Axiom cannot compute this integral
  14:272 Axiom cannot simplify these expressions
  14:273 Schaums and Axiom differ by a constant
  14:274 Schaums and Axiom agree
  14:275 Axiom cannot compute this integral
  14:276 Axiom cannot compute this integral
  14:277 Schaums and Axiom differ by a constant
  14:278 Schaums and Axiom differ by a constant
  14:279 Axiom cannot compute this integral
  14:280 Axiom cannot simplify these expressions
  14:281 Axiom cannot simplify these expressions
  14:282 Axiom cannot simplify these expressions
  14:283 Axiom cannot simplify these expressions
  14:284 Axiom cannot simplify these expressions
  14:284 Axiom cannot simplify these expressions
  14:285 Axiom cannot simplify these expressions
  14:286 Axiom cannot simplify these expressions
  14:287 Axiom cannot simplify these expressions
  14:288 Axiom cannot simplify these expressions
  14:289 Axiom cannot simplify these expressions
  14:290 Axiom cannot simplify these expressions
  14:291 Axiom cannot simplify these expressions
  14:292 Axiom cannot simplify these expressions
  14:293 Axiom cannot simplify these expressions
  14:295 Axiom cannot compute this integral
  14:296 Axiom cannot compute this integral
  14:297 Axiom cannot compute this integral
  14:298 Axiom cannot compute this integral
  14:299 Schaums and Axiom agree
  14:300 Schaums and Axiom agree
  14:301 Schaums and Axiom agree
  14:302 Schaums and Axiom agree
  14:303 Schaums and Axiom agree
  14:304 Schaums and Axiom agree
  14:305 Schaums and Axiom agree
  14:306 Schaums and Axiom agree
  14:307 Schaums and Axiom agree
  14:308 Schaums and Axiom agree
  14:309 Axiom cannot compute this integral
  14:310 Axiom cannot compute this integral
  14:311 Schaums and Axiom differ by a constant
  14:312 Schaums and Axiom agree
  14:313 Schaums and Axiom differ by a constant
  14:314 Schaums and Axiom agree
  14:315 Schaums and Axiom agree
  14:316 Schaums and Axiom differ by a constant
  14:317 Schaums and Axiom agree
  14:318 Schaums and Axiom agree
  14:319 Schaums and Axiom agree
  14:320 Schaums and Axiom agree
  14:321 Schaums and Axiom agree
  14:322 Schaums and Axiom agree
  14:323 Schaums and Axiom agree
  14:324 Schaums and Axiom agree
  14:325 Axiom cannot simplify this expression
  14:326 Schaums and Axiom agree
  14:327 Axiom cannot compute this integral
  14:328 Axiom cannot compute this integral
  14:329 Schaums and Axiom differ by a constant
  14:330 Schaums and Axiom agree
  14:331 Schaums and Axiom agree
  14:332 Axiom cannot compute this integral
  14:333 Axiom cannot compute this integral
  14:334 Axiom cannot simplify this expression
  14:335 Axiom cannot compute this integral
  14:336 Axiom cannot compute this integral
  14:337 Axiom cannot compute this integral
  14:338 Axiom cannot compute this integral
  14:339 Schaums and Axiom agree
  14:340 Schaums and Axiom agree
  14:341 Schaums and Axiom agree
  14:342 Schaums and Axiom agree
  14:343 Schaums and Axiom agree by definition
  14:344 Axiom cannot compute this integral
  14:345 Schaums and Axiom agree
  14:346 Axiom cannot compute this integral
  14:347 Schaums and Axiom agreee
  14:348 Schaums and Axiom differ by a constant
  14:349 Schaums and Axiom agree
  14:350 Schaums and Axiom agree
  14:351 Schaums and Axiom agree
  14:352 Schaums and Axiom agree
  14:353 Axiom cannot simplify this expression
  14:354 Schaums and Axiom differ by a constant
  14:355 Axiom cannot simplify this expression
  14:356 Axiom cannot simplify this expression
  14:357 Axiom cannot simplify this expression
  14:358 Axiom cannot simplify this expression
  14:359 Axiom cannot simplify this expression
  14:360 Axiom cannot simplify these equations
  14:361 Schaums and Axiom differ by a constant
  14:362 Axiom cannot simplify this expression
  14:363 Axiom cannot simplify this expression
  14:364 Axiom cannot compute this integral
  14:365 Axiom cannot compute this integral
  14:366 Axiom cannot compute this integral
  14:367 Axiom cannot compute this integral
  14:368 Axiom cannot compute this integral
  14:369 Schaums and Axiom agree
  14:370 Schaums and Axiom agree
  14:371 Schaums and Axiom agree
  14:372 Schaums and Axiom agree
  14:373 Schaums and Axiom agree by definition
  14:374 Axiom cannot compute this integral
  14:375 Axiom cannot simplify these expressions
  14:376 Axiom cannot compute this integral
  14:377 Schaums and Axiom agree
  14:378 Schaums and Axiom differ by a constant
  14:379 Schaums and Axiom agree
  14:380 Axiom cannot simplify this expression
  14:381 Schaums and Axiom agree
  14:382 Axiom cannot simplify this expression
  14:383 Axiom cannot simplify this expression
  14:384 Axiom cannot simplify this expression
  14:385 Axiom cannot simplify this expression
  14:386 Axiom cannot simplify this expression
  14:387 Axiom cannot simplify this expression
  14:388 Axiom cannot simplify this expression
  14:389 Axiom cannot simplify this expression
  14:390 Axiom cannot simplify these expressions
  14:391 Schaums and Axiom agree
  14:392 Axiom cannot simplify these expressions
  14:393 Axiom cannot simplify these expressions
  14:394 Axiom cannot compute this integral
  14:395 Axiom cannot compute this integral
  14:396 Axiom cannot compute this integral
  14:397 Axiom cannot compute this integral
  14:398 Axiom cannot compute this integral
  14:399 Schaums and Axiom differ by a constant
  14:400 Axiom is unable to simplify this expression
  14:401 Schaums and Axiom agree
  14:402 Schaums and Axiom agree
  14:403 Schaums and Axiom agree
  14:404 Schaums and Axiom differ by a constant
  14:405 Schaums and Axiom differ by a constant
  14:406 Schaums and Axiom differ by a constant
  14:407 Schaums and Axiom agree
  14:408 Schaums and Axiom differ by a constant
  14:409 Schaums and Axiom agree
  14:410 Schaums and Axiom differ by a constant
  14:411 Schaums and Axiom differ by a constant
  14:412 Axiom cannot simplify this expression
  14:413 Schaums and Axiom agree
  14:414 Schaums and Axiom agree
  14:415 Schaums and Axiom differ by a constant
  14:416 Schaums and Axiom agree
  14:417 Schaums and Axiom agree
  14:418 Schaums and Axiom agree
  14:419 Axiom cannot simplify this expression
  14:420 Axiom cannot simplify these expressions
  14:421 Schaums and Axiom agree
  14:422 Axiom cannot simplify this expression
  14:423 Axiom cannot simplify this expressions
  14:424 Schaums and Axiom differ by a constant
  14:425 Axiom cannot compute this integral
  14:426 Axiom cannot compute this integral
  14:427 Axiom cannot compute this integral
  14:428 Axiom cannot compute this integral
  14:429 Schaums and Axiom agree
  14:430 Schaums and Axiom agree
  14:431 Schaums and Axiom agree
  14:432 Schaums and Axiom agree
  14:433 Schaums and Axiom differ by a constant
  14:435 Axiom cannot compute this integral
  14:436 Axiom cannot compute this integral
  14:437 Schaums and Axiom agree
  14:438 Schaums and Axiom agree
  14:439 Axiom cannot compute this integral
  14:440 Schaums and Axiom agree
  14:441 Schaums and Axiom agree
  14:442 Schaums and Axiom agree
  14:443 Schaums and Axiom agree
  14:444 Schaums and Axiom differ by a constant
  14:445 Schaums and Axiom agree
  14:446 Axiom cannot compute this integral
  14:447 Axiom cannot compute this integral
  14:448 Schaums and Axiom agree
  14:449 Axiom cannot simplify this expression
  14:450 Axiom cannot compute this integral
  14:451 Schaums and Axiom differ by a constant
  14:452 Schaums and Axiom agree
  14:453 Schaums and Axiom differ by a constant
  14:454 Axiom cannot simplify this expression
  14:455 Schaums and Axiom agree
  14:456 Axiom cannot compute this integral
  14:457 Axiom cannot compute this integral
  14:458 Schaums and Axiom differ by a constant
  14:459 Schaums and Axiom agree
  14:460 Axiom cannot compute this integral
  14:461 Schaums and Axiom agree
  14:462 Schaums and Axiom agree
  14:463 Schaums and Axiom agree
  14:464 Axiom cannot simplify this expression
  14:465 Schaums and Axiom agree
  14:466 Axiom cannot compute this integral
  14:467 Axiom cannot compute this integral
  14:468 Schaums and Axiom differ by a constant
  14:469 Schaums and Axiom agree
  14:470 Axiom cannot compute this integral
  14:471 Axiom cannot simplify this expression
  14:472 Axiom cannot simplify this expression
  14:473 Axiom cannot simplify this expression
  14:474 Axiom cannot compute this integral
  14:475 Axiom cannot simplify this expression
  14:476 Axiom cannot simplify this expression
  14:477 Axiom cannot simplify this expression
  14:478 Axiom cannot simplify this expression
  14:479 Axiom cannot simplify this expression
  14:480 Axiom cannot compute this integral
  14:481 Axiom cannot simplify this expression
  14:482 Axiom cannot simplify this expression
  14:483 SCHAUMS AND AXIOM DIFFER? (BRANCH CUTS?)
  14:484 Axiom cannot compute this integral
  14:485 Axiom cannot simplify this expression
  14:486 Axiom cannot compute this integral
  14:487 SCHAUMS AND AXIOM DIFFER? (branch cuts?)
  14:488 Axiom and Schaums agree
  14:489 Axiom and Schaums agree
  14:490 Axiom and Schaums agree
  14:491 Axiom cannot compute this integral
  14:492 Schaums and Axiom agree
  14:493 Axiom cannot simplify these expressions
  14:494 Axiom cannot simplify these expressions
  14:495 Axiom cannot simplify these expressions
  14:496 Axiom cannot compute this integral
  14:497 Axiom cannot simplify these expressions
  14:498 Axiom cannot simplify these expressions
  14:499 Axiom cannot simplify these expressions
  14:500 Axiom cannot simplify this expression
  14:501 Axiom cannot compute this integral
  14:502 Axiom cannot simplify this expression
  14:503 Axiom cannot compute this integral
  14:504 Axiom cannot compute this integral
  14:505 SCHAUMS AND AXIOM DISAGREE? (branch cuts?)
  14:506 Axiom cannot compute this integral
  14:507 Axiom cannot compute this integral
  14:508 Axiom cannot compute this integral
  14:509 Schaums and Axiom agree
  14:510 Schaums and Axiom agree
  14:511 Schaums and Axiom agree
  14:512 Axiom cannot compute this integral
  14:513 Schaums and Axiom agree by definition
  14:514 Axiom cannot compute this integral
  14:515 Schaums and Axiom agree
  14:516 Schaums and Axiom agree
  14:517 Axiom cannot simplify these expressions
  14:518 Schaums and Axiom agree
  14:519 Schaums and Axiom agree
  14:520 Schaums and Axiom agree
  14:521 Schaums and Axiom agree
  14:522 Schaums and Axiom agree by definition
  14:523 Axiom cannot compute this integral
  14:524 Axiom cannot compute this integral
  14:525 Schaums and Axiom agree
  14:526 Schaums and Axiom agree
  14:527 Schaums and Axiom agree
  14:528 Schaums and Axiom agree
  14:529 Schaums and Axiom agree
  14:530 Schaums and Axiom agree
  14:531 Schaums and Axiom agree
  14:532 Schaums and Axiom agree
  14:533 Schaums and Axiom agree by definition
  14:534 Axiom cannot compute this integral
  14:535 Axiom cannot compute this integral
  14:536 Axiom cannot compute this integral
  14:537 Schaums and Axiom agree
  14:538 Schaums and Axiom agree
  14:539 Axiom cannot compute this integral
  14:540 Schaums and Axiom agree
  14:541 Schaums and Axiom agree
  14:542 Schaums and Axiom agree
  14:543 Axiom cannot compute this integral
  14:544 Axiom cannot compute this integral
  14:545 Axiom cannot simplify this expression
  14:546 Axiom cannot compute this integral
  14:547 Schaums and Axiom agree
  14:548 Schaums and Axiom agree
  14:549 Schaums and Axiom differ by a constant
  14:550 Axiom cannot simplify this expression
  14:551 Schaums and Axiom agree
  14:552 Schaums and Axiom agree
  14:553 Axiom cannot simplify this expression
  14:554 Axiom cannot simplify this expression
  14:555 Axiom cannot simplify this expression
  14:556 Axiom cannot simplify this expression
  14:557 Axiom cannot compute this integral
  14:558 Axiom cannot compute this integral
  14:559 Axiom cannot compute this integral
  14:560 Axiom cannot compute this integral
  14:561 Axiom cannot compute this integral
  14:562 Schaums and Axiom agree
  14:563 Schaums and Axiom agree
  14:564 Schaums and Axiom agree
  14:565 Axiom cannot compute this integral
  14:566 Axiom cannot compute this integral
  14:567 Schaums and Axiom agree
  14:568 Axiom cannot compute this integral
  14:569 Schaums and Axiom agree
  14:570 Schaums and Axiom agree
  14:571 Schaums and Axiom differ by a constant
  14:572 Axiom cannot simplify this expression
  14:573 Schaums and Axiom agree
  14:574 Schaums and Axiom agree
  14:575 Schaums and Axiom differ by a constant
  14:576 Schaums and Axiom differ by a constant
  14:577 Schaums and Axiom differ by a constant
  14:578 Schaums and Axiom differ by a constant
  14:579 Axiom cannot compute this integral
  14:580 Axiom cannot simplify this expression
  14:581 Axiom cannot simplify this expression
  14:582 Axiom cannot simplify this expression
  14:583 Axiom cannot simplify this expression
  14:584 Axiom cannot simplify this expression
  14:585 Axiom cannot compute this integral
  14:586 Axiom cannot compute this integral
  14:587 Axiom cannot compute this integral
  14:588 Axiom cannot compute this integral
  14:589 Axiom cannot compute this integral
  14:590 Schaums and Axiom differ by a constant
  14:591 Axiom cannot simplify this expression
  14:592 Axiom cannot simplify this expression
  14:593 Axiom cannot simplify this expression
  14:594 Schaums and Axiom agree
  14:595 Schaums and Axiom agree
  14:596 Axiom cannot simplify this expression
  14:597 Schaums and Axiom agree
  14:598 Axiom cannot simplify this expression
  14:599 Axiom cannot simplify this expression
  14:600 Axiom cannot simplify this expression
  14:601 Schaums and Axiom agree
  14:602 Schaums and Axiom agree
  14:603 Schaums and Axiom agree
  14:604 Schaums and Axiom differ by a constant
  14:605 Schaums and Axiom differ by a constant
  14:606 Axiom cannot simplify this expression
  14:607 Axiom cannot simplify this expression
  14:608 Schaums and Axiom agree
  14:609 Schaums and Axiom differ by a constant
  14:610 Axiom cannot compute this integral
  14:611 Schaums and Axiom differ by a constant
  14:612 Axiom cannot compute this integral
  14:613 Schaums and Axiom differ by a constant
  14:614 Axiom cannot compute this integral
  14:615 Schaums and Axiom differ by a constant
  14:616 Schaums and Axiom differ by a constant
  14:617 Axiom cannot simplify this expression
  14:618 Schaums and Axiom agree
  14:619 Schaums and Axiom agree
  14:620 Schaums and Axiom differ by a constant
  14:621 Axiom cannot compute this integral
  14:622 Schaums and Axiom differ by a constant
  14:623 Axiom cannot compute this integral
  14:624 Schaums and Axiom differ by a constant
  14:625 Axiom cannot compute this integral
  14:626 Schaums and Axiom agree
  14:627 Schaums and Axiom differ by a constant
  14:628 Axiom cannot simplify this expression
  14:629 Schaums and Axiom agree
  14:630 Schaums and Axiom agree
  14:631 Axiom cannot compute this integral
  14:632 Schaums and Axiom differ by a constant
  14:633 Axiom cannot compute this integral
  14:634 Schaums and Axiom agree
  14:635 Axiom cannot compute this integral
  14:636 Schaums and Axiom agree
  14:637 Axiom cannot simplify this expression
  14:638 Axiom cannot simplify this expression
  14:639 Schaums and Axiom agree
  14:640 Schaums and Axiom agree
  14:641 Axiom cannot compute this integral
  14:642 Schaums and Axiom differ by a constant
  14:643 Axiom cannot compute this integral
  14:644 Schaums and Axiom differ by a constant
  14:645 Axiom cannot compute this integral
  14:646 Schaums and Axiom agree
  14:647 Schaums and Axiom agree
  14:648 Schaums and Axiom agree
  14:649 Axiom cannot compute this integral
  14:650 Schaums and Axiom differ by a constant
  14:651 Schaums and Axiom agree
  14:652 Schaums and Axiom agree
  14:653 Schaums and Axiom agree
  14:654 Axiom cannot compute this integral
  14:655 Axiom cannot simplify these expressions
  14:656 Schaums and Axiom differ by a constant
  14:657 Schaums and Axiom agree
  14:658 Schaums and Axiom differ by a constant
  14:659 Axiom cannot compute this integral
  14:660 Schaums and Axiom agree
  14:661 Schaums and Axiom agree
  14:662 Schaums and Axiom agree
  14:663 Schaums and Axiom agree
  14:664 Axiom cannot compute this integral
  14:665 Schaums and Axiom agree
  14:666 Schaums and Axiom agree
  14:667 Schaums and Axiom differ by a constant
  14:668 SCHAUMS AND AXIOM DIFFER (Axiom has closed form)
  14:669 Axiom cannot simplify these expressions
  14:670 Axiom cannot simplify these expressions
  14:671 SCHAUMS AND AXIOM DIFFER (Axiom has closed form)
  14:672 Axiom cannot compute this integral
  14:673 Axiom cannot compute this integral
  14:674 Axiom cannot compute this integral
  14:675 Axiom cannot compute this integral
  14:676 Axiom cannot compute this integral
  14:677 Axiom cannot compute this integral


  



   




reply via email to

[Prev in Thread] Current Thread [Next in Thread]