-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy path6.5.10 (c+d x)^m (a+b sech)^n.nb
More file actions
536 lines (521 loc) · 27 KB
/
6.5.10 (c+d x)^m (a+b sech)^n.nb
File metadata and controls
536 lines (521 loc) · 27 KB
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
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
(* Content-type: application/mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 7.0' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 145, 7]
NotebookDataLength[ 26885, 527]
NotebookOptionsPosition[ 24857, 465]
NotebookOutlinePosition[ 26573, 519]
CellTagsIndexPosition[ 26530, 516]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
StyleBox[
RowBox[{Cell[TextData[StyleBox["Rules for integrands of the form",
FontFamily->"Arial",
FontSize->16]], "None"],
SuperscriptBox[
RowBox[{"(",
RowBox[{"c", "+",
RowBox[{"d", " ", "x"}]}], ")"}], "m"], " ",
SuperscriptBox[
RowBox[{"(",
RowBox[{"a", "+",
RowBox[{"b", " ",
RowBox[{"Sech", "[",
RowBox[{"e", "+",
RowBox[{"f", " ", "x"}]}], "]"}]}]}], ")"}], "n"]}],
FontSize->16]], "Subsubtitle",
CellDingbat->None,
CellChangeTimes->{
3.477935275784027*^9, {3.477935350060832*^9, 3.477935352384173*^9}, {
3.477935393803731*^9, 3.477935400102789*^9}, {3.477935515378547*^9,
3.47793552034569*^9}, 3.478120029940968*^9, {3.479318860690858*^9,
3.47931886615872*^9}, {3.4794185033278093`*^9, 3.479418503918659*^9},
3.4795122294117584`*^9, {3.479615913307893*^9, 3.4796159352794867`*^9},
3.4796160386581373`*^9, 3.4796867204045024`*^9, {3.4928025699585147`*^9,
3.492802570130115*^9}, 3.492822274480175*^9, 3.492825822242408*^9, {
3.4940970615585365`*^9, 3.494097062168537*^9}, {3.496441349250718*^9,
3.496441349830719*^9}, 3.4964414848609076`*^9, 3.496521708137803*^9, {
3.4965218981240697`*^9, 3.49652189838407*^9}, 3.4965229070755*^9,
3.519247079685614*^9, {3.5193208582062006`*^9, 3.5193208612170057`*^9},
3.5193325694253187`*^9, {3.5193415004828687`*^9, 3.5193415113404875`*^9}, {
3.5193513965602303`*^9, 3.519351397420232*^9}, {3.5194037839416766`*^9,
3.5194037847117205`*^9}, {3.5233155055329347`*^9, 3.523315506402936*^9}, {
3.523318726949605*^9, 3.5233187276796064`*^9}, {3.523920400879534*^9,
3.5239204094439487`*^9}, 3.52392096260852*^9, 3.523921038171853*^9,
3.5340477459008017`*^9, 3.5340515540554085`*^9, {3.536542511100503*^9,
3.53654251626051*^9}, {3.536775961244521*^9, 3.5367759616145215`*^9}, {
3.544373142375139*^9, 3.5443731599851637`*^9}, {3.5721095751430073`*^9,
3.5721095751430073`*^9}, {3.57578648209792*^9, 3.575786503859958*^9},
3.575786540270422*^9, {3.5757866379421935`*^9, 3.5757866609522343`*^9},
3.5758478960540276`*^9, 3.6740841648958893`*^9, 3.674496270639579*^9},
TextAlignment->Center,
FontSize->12,
FontWeight->"Bold"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{Cell[TextData[StyleBox["N:",
FontFamily->"Arial",
FontColor->RGBColor[1, 0, 0]]], "None"], " ",
RowBox[{"\[Integral]",
RowBox[{
SuperscriptBox["u", "m"],
SuperscriptBox[
RowBox[{"Sech", "[", "v", "]"}], "n"],
RowBox[{"\[DifferentialD]", "x"}], " ",
StyleBox["when",
FontFamily->"Arial",
FontWeight->"Plain"],
StyleBox[" ",
FontFamily->"Arial",
FontWeight->"Plain"], Cell[TextData[Cell[BoxData[
RowBox[{
RowBox[{"u", "\[Equal]",
RowBox[{"c", "+",
RowBox[{"d", " ", "x"}]}]}], " ", "\[And]", " ",
RowBox[{"v", "\[Equal]",
RowBox[{"a", "+",
RowBox[{"b", " ", "x"}]}]}]}]]]], "None"]}]}]}]], "Subsubtitle",
CellDingbat->None,
CellChangeTimes->{
3.477935275784027*^9, {3.477935350060832*^9, 3.477935352384173*^9}, {
3.477935393803731*^9, 3.477935400102789*^9}, {3.477935515378547*^9,
3.47793552034569*^9}, 3.478120029940968*^9, {3.479318860690858*^9,
3.47931886615872*^9}, {3.4794185033278093`*^9, 3.479418503918659*^9},
3.4795122294117584`*^9, {3.479615913307893*^9, 3.4796159352794867`*^9},
3.4796160386581373`*^9, 3.4796867204045024`*^9, {3.4928025699585147`*^9,
3.492802570130115*^9}, 3.492822274480175*^9, 3.492825822242408*^9, {
3.4940970615585365`*^9, 3.494097062168537*^9}, {3.496441349250718*^9,
3.496441349830719*^9}, 3.4964414848609076`*^9, 3.4964645213514385`*^9,
3.5192470594155855`*^9, {3.519247288125906*^9, 3.5192473207459517`*^9}, {
3.519247363296011*^9, 3.519247363796012*^9}, 3.519258420199427*^9,
3.5192584863895197`*^9, {3.519320760160028*^9, 3.519320767367241*^9},
3.5193299099191504`*^9, {3.5193300315093203`*^9, 3.519330031709321*^9}, {
3.5193323099968634`*^9, 3.5193324414114943`*^9}, {3.5193327317904043`*^9,
3.519332762148057*^9}, {3.519340455685931*^9, 3.519340463318947*^9},
3.519340635545749*^9, {3.5193422478304834`*^9, 3.519342248704085*^9}, {
3.519342492766513*^9, 3.519342493156514*^9}, {3.519345750301442*^9,
3.5193457505978427`*^9}, 3.519346263464343*^9, {3.519349307658399*^9,
3.519349310965605*^9}, {3.519352294781488*^9, 3.5193522950014887`*^9}, {
3.5194134359455075`*^9, 3.519413446054325*^9}, {3.5194134908888044`*^9,
3.5194134927764077`*^9}, {3.5194141847624226`*^9,
3.5194142323581066`*^9}, {3.519414342899901*^9, 3.519414474720132*^9}, {
3.5197939535480833`*^9, 3.5197939539380836`*^9}, {3.5197940297698174`*^9,
3.5197940299726176`*^9}, 3.519795153580191*^9, {3.5200103027397947`*^9,
3.5200103044997973`*^9}, {3.5232186878169007`*^9,
3.5232186881569014`*^9}, {3.5232193955778913`*^9,
3.5232193955778913`*^9}, {3.5233166487845354`*^9,
3.5233166487845354`*^9}, {3.5233167010346084`*^9,
3.5233167010346084`*^9}, {3.523318546315711*^9, 3.523318573368556*^9}, {
3.5239220709492664`*^9, 3.5239220924617043`*^9}, {3.5239221279205666`*^9,
3.5239221365629816`*^9}, {3.523930270899587*^9, 3.523930270899587*^9}, {
3.5240761703528385`*^9, 3.5240761703528385`*^9}, {3.52407843124921*^9,
3.5240784332304134`*^9}, {3.5240784932749186`*^9,
3.5240784932749186`*^9}, {3.524079230095413*^9, 3.524079246553442*^9}, {
3.5240858499762287`*^9, 3.524085860178646*^9}, {3.524085945261196*^9,
3.524085945261196*^9}, {3.5242763399632483`*^9, 3.5242763411488504`*^9}, {
3.5242771575294847`*^9, 3.5242771578102846`*^9}, {3.530500224433988*^9,
3.530500225113989*^9}, {3.5313467876910577`*^9, 3.5313467883119507`*^9}, {
3.5332231066826243`*^9, 3.5332231066826243`*^9}, {3.5332248881251183`*^9,
3.533224890245121*^9}, {3.5361011385491977`*^9, 3.5361011394332485`*^9}, {
3.5363501469745007`*^9, 3.5363501506345057`*^9}, {3.5363617411167684`*^9,
3.5363617534067855`*^9}, {3.536366615151597*^9, 3.5363666230616083`*^9}, {
3.5363667754518213`*^9, 3.5363667821318307`*^9}, {3.536366906722005*^9,
3.536366922022027*^9}, {3.536596861742076*^9, 3.5365968701504908`*^9}, {
3.5366042542749715`*^9, 3.536604254462172*^9}, {3.536625554425806*^9,
3.536625554775807*^9}, {3.5366276426139326`*^9, 3.536627642853933*^9}, {
3.536629402336396*^9, 3.536629402746397*^9}, {3.5366940603006477`*^9,
3.536694061273703*^9}, {3.5366943323932104`*^9, 3.536694332661226*^9}, {
3.536694390476533*^9, 3.536694402176202*^9}, {3.5368634751022315`*^9,
3.5368634756170325`*^9}, {3.536980474148706*^9, 3.5369804925387316`*^9}, {
3.5369807910591497`*^9, 3.5369808136991816`*^9}, 3.538443999546241*^9, {
3.538444040229568*^9, 3.5384440801737804`*^9}, {3.544471201864182*^9,
3.5444712020241823`*^9}, {3.5499343621399236`*^9,
3.5499343628887253`*^9}, {3.5693429012648573`*^9, 3.569342923814889*^9}, {
3.5693432071452856`*^9, 3.5693432074652863`*^9}, {3.569351915062778*^9,
3.569351927142795*^9}, {3.569352555713675*^9, 3.569352597773734*^9}, {
3.5694315155137024`*^9, 3.569431516203704*^9}, {3.5748842843912826`*^9,
3.5748842879212875`*^9}, {3.5748843600113883`*^9, 3.574884366281397*^9},
3.5748844907815714`*^9, {3.574884521101614*^9, 3.5748845214216146`*^9},
3.590638001724437*^9, {3.673567804677744*^9, 3.673567804842753*^9},
3.6739034525366917`*^9, 3.6739043270907135`*^9, {3.6739044139566813`*^9,
3.673904414164694*^9}, 3.6740842975654783`*^9, {3.6970866197576513`*^9,
3.697086620046668*^9}},
FontSize->12,
FontWeight->"Bold"],
Cell["Derivation: Algebraic normalization", "Subsubsection",
CellChangeTimes->{
3.4953915070313115`*^9, 3.495840214754669*^9, {3.4958483177760134`*^9,
3.495848318886015*^9}, {3.495925911922002*^9, 3.495925920122013*^9},
3.4961847242848682`*^9, 3.496184957525194*^9, 3.496188449500083*^9,
3.4961908979261436`*^9, 3.4961924998683863`*^9, 3.4961928754389124`*^9, {
3.51849075797458*^9, 3.5184907698562593`*^9}, 3.574710542770027*^9}],
Cell[TextData[{
"Rule: If ",
Cell[BoxData[
RowBox[{
RowBox[{"u", "\[Equal]",
RowBox[{"c", "+",
RowBox[{"d", " ", "x"}]}]}], " ", "\[And]", " ",
RowBox[{"v", "\[Equal]",
RowBox[{"a", "+",
RowBox[{"b", " ", "x"}]}]}]}]]],
", then"
}], "Subsubsection",
CellDingbat->"\[FilledSmallSquare]",
CellChangeTimes->{{3.4794189093216*^9, 3.479418932274605*^9}, {
3.479418981395237*^9, 3.4794189822564754`*^9}, {3.4794192068193808`*^9,
3.4794192077607346`*^9}, 3.479420089138093*^9, {3.479420130978256*^9,
3.4794201410627565`*^9}, {3.479420560345656*^9, 3.479420578171288*^9}, {
3.479420683943381*^9, 3.4794206847645617`*^9}, {3.4794210347678413`*^9,
3.4794210503903055`*^9}, 3.4803613662913427`*^9, {3.480361406058525*^9,
3.48036141974821*^9}, {3.4803614672865667`*^9, 3.480361474717252*^9},
3.4807050675119123`*^9, {3.495391630941485*^9, 3.4953916682515373`*^9},
3.495398892616804*^9, {3.495402251391507*^9, 3.4954022711315346`*^9}, {
3.495488783827441*^9, 3.4954888500775337`*^9}, {3.4954889799777155`*^9,
3.495489009627757*^9}, {3.495489141407942*^9, 3.495489151717956*^9}, {
3.495489235178073*^9, 3.495489239268079*^9}, {3.495489386068284*^9,
3.4954894212383337`*^9}, {3.495489464438394*^9, 3.4954894647383947`*^9}, {
3.495489500148444*^9, 3.4954895034984484`*^9}, {3.4954897331687703`*^9,
3.495489780118836*^9}, {3.495493913565876*^9, 3.495493935715907*^9}, {
3.495494084919718*^9, 3.4954941083997507`*^9}, 3.495494511560315*^9, {
3.495494580840412*^9, 3.4954945834404163`*^9}, {3.495494615970462*^9,
3.495494740200636*^9}, {3.495494880710832*^9, 3.4954948880508423`*^9}, {
3.4954949819649754`*^9, 3.495494999445*^9}, {3.495495046515066*^9,
3.495495072875103*^9}, {3.4954951239351745`*^9, 3.4954951241651745`*^9}, {
3.4954953673051157`*^9, 3.4954953726551237`*^9}, {3.495495450474448*^9,
3.495495453173253*^9}, {3.495495542140209*^9, 3.495495583792282*^9}, {
3.4954957431465626`*^9, 3.4954957746118174`*^9}, {3.495495914419263*^9,
3.495495917804469*^9}, {3.495495955322535*^9, 3.4954960459586945`*^9}, {
3.495496189588146*^9, 3.4954961923181515`*^9}, {3.4954973384365644`*^9,
3.495497357577798*^9}, {3.5240858715198665`*^9, 3.52408591925595*^9}, {
3.5331536712917595`*^9, 3.5331536971617956`*^9}, {3.533223063022563*^9,
3.5332230658125668`*^9}, {3.533224894045127*^9, 3.5332248954551287`*^9},
3.5363501685345306`*^9, {3.538444353705845*^9, 3.5384443676658645`*^9}, {
3.5499343655595293`*^9, 3.549934366379531*^9}, {3.5693429326149015`*^9,
3.5693429326149015`*^9}, {3.5693520880530205`*^9,
3.5693520882530203`*^9}, {3.5693526036737423`*^9,
3.5693526036737423`*^9}, {3.5748843707814035`*^9, 3.5748843707814035`*^9}}],
Cell[BoxData[
RowBox[{"\[Integral]",
RowBox[{
SuperscriptBox["u", "m"],
SuperscriptBox[
RowBox[{"Sech", "[", "v", "]"}], "n"],
RowBox[{"\[DifferentialD]",
RowBox[{"x", " ", "\[LongRightArrow]", " ",
RowBox[{"\[Integral]",
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"c", "+",
RowBox[{"d", " ", "x"}]}], ")"}], "m"], " ",
SuperscriptBox[
RowBox[{"Sech", "[",
RowBox[{"a", "+",
RowBox[{"b", " ", "x"}]}], "]"}], "n"],
RowBox[{"\[DifferentialD]", "x"}]}]}]}]}]}]}]], "Subsubtitle",
CellDingbat->None,
CellChangeTimes->{{3.4796579723816*^9, 3.4796580261689425`*^9},
3.479661191290163*^9, {3.479686720164157*^9, 3.479686720204214*^9}, {
3.479686831554328*^9, 3.479686834819022*^9}, {3.4940970712485504`*^9,
3.4940971130286083`*^9}, 3.4940971455886545`*^9, 3.4953915848214207`*^9,
3.495391696001576*^9, {3.495401987881138*^9, 3.49540199674115*^9}, {
3.495402119591322*^9, 3.4954021482513623`*^9}, {3.4954887467773895`*^9,
3.4954887749874287`*^9}, 3.495488944397666*^9, 3.495489263778113*^9,
3.4954893636582527`*^9, 3.4954898177188883`*^9, 3.495489875358969*^9,
3.495493833545764*^9, 3.495493864175807*^9, 3.4954940303560395`*^9,
3.4954941516698112`*^9, 3.4954942700599775`*^9, 3.4954948473707857`*^9, {
3.495495264965372*^9, 3.4954952782653904`*^9}, {3.4954956850364604`*^9,
3.4954957088577023`*^9}, {3.495495865341577*^9, 3.4954958884920177`*^9}, {
3.495496084225561*^9, 3.4954961029143944`*^9}, {3.495496211459385*^9,
3.4954962213810024`*^9}, 3.495496440218187*^9, {3.495497026732417*^9,
3.4954970596328745`*^9}, {3.495497256957621*^9, 3.495497302338101*^9},
3.533151648818928*^9, 3.5331516797189713`*^9, 3.533151717349024*^9, {
3.5331518776292486`*^9, 3.533151970249378*^9}, {3.5331520176994443`*^9,
3.5331520227894516`*^9}, {3.533152054329496*^9, 3.5331520626995077`*^9},
3.533152270349798*^9, {3.533153065130911*^9, 3.5331530971109557`*^9},
3.53315335008131*^9, {3.5331535194015465`*^9, 3.5331535356615696`*^9},
3.5331536017616625`*^9, {3.533221927890974*^9, 3.533221930830978*^9}, {
3.533222264011444*^9, 3.533222283731472*^9}, {3.5332223304615374`*^9,
3.5332223353515444`*^9}, 3.5363501604045196`*^9, {3.536361767566806*^9,
3.5363617697768087`*^9}, {3.5363666287016163`*^9,
3.5363666313816195`*^9}, {3.536366784271834*^9, 3.5363667868618374`*^9}, {
3.536366923782029*^9, 3.5363669254320316`*^9}, {3.5365968786057057`*^9,
3.536596881944112*^9}, {3.5366940930205193`*^9, 3.53669410440917*^9}, {
3.5366942507975435`*^9, 3.536694251403578*^9}, {3.536694493325415*^9,
3.536694495295528*^9}, 3.536980387788585*^9, {3.5384441491255584`*^9,
3.538444158185571*^9}, 3.5384445157160716`*^9, {3.5693429405449123`*^9,
3.569342962434943*^9}, {3.5693520924330263`*^9, 3.5693520926030264`*^9}, {
3.5693526191837635`*^9, 3.569352629573778*^9}, {3.5748843099713182`*^9,
3.574884350491375*^9}, {3.673904336743265*^9, 3.6739043383933597`*^9}, {
3.6740842981665125`*^9, 3.674084298630539*^9}},
TextAlignment->Center,
FontSize->12,
FontWeight->"Bold"],
Cell["Program code:", "Subsubsection",
CellDingbat->"\[FilledSmallSquare]",
CellChangeTimes->{{3.4794189093216*^9, 3.479418932274605*^9}, {
3.479418981395237*^9, 3.4794189822564754`*^9}, {3.4794192068193808`*^9,
3.4794192077607346`*^9}, 3.479420089138093*^9, {3.479420130978256*^9,
3.4794201410627565`*^9}, {3.479420560345656*^9, 3.479420578171288*^9}, {
3.479420683943381*^9, 3.4794206847645617`*^9}, {3.4794210347678413`*^9,
3.4794210503903055`*^9}, 3.4803613662913427`*^9, {3.480361406058525*^9,
3.48036141974821*^9}, {3.4803614672865667`*^9, 3.480361474717252*^9},
3.4807050675119123`*^9, {3.492804314166378*^9, 3.4928043441496305`*^9}, {
3.4928044532166224`*^9, 3.492804453513023*^9}, {3.492805162266266*^9,
3.492805165713872*^9}}],
Cell[BoxData[
RowBox[{
RowBox[{"Int", "[",
RowBox[{
RowBox[{
RowBox[{"u_", "^", "m_."}], "*",
RowBox[{
RowBox[{"Sech", "[", "v_", "]"}], "^", "n_."}]}], ",", "x_Symbol"}],
"]"}], " ", ":=", "\n", " ",
RowBox[{
RowBox[{"Int", "[",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"ExpandToSum", "[",
RowBox[{"u", ",", "x"}], "]"}], "^", "m"}], "*",
RowBox[{
RowBox[{"Sech", "[",
RowBox[{"ExpandToSum", "[",
RowBox[{"v", ",", "x"}], "]"}], "]"}], "^", "n"}]}], ",", "x"}],
"]"}], " ", "/;", "\n",
RowBox[{
RowBox[{"FreeQ", "[",
RowBox[{
RowBox[{"{",
RowBox[{"m", ",", "n"}], "}"}], ",", "x"}], "]"}], " ", "&&", " ",
RowBox[{"LinearQ", "[",
RowBox[{
RowBox[{"{",
RowBox[{"u", ",", "v"}], "}"}], ",", "x"}], "]"}], " ", "&&", " ",
RowBox[{"Not", "[",
RowBox[{"LinearMatchQ", "[",
RowBox[{
RowBox[{"{",
RowBox[{"u", ",", "v"}], "}"}], ",", "x"}], "]"}],
"]"}]}]}]}]], "Code",
CellChangeTimes->{{3.494097165958683*^9, 3.4940971894087152`*^9}, {
3.4940972668388243`*^9, 3.4940972723188314`*^9}, 3.49539148440128*^9,
3.4954018196509027`*^9, {3.495401867050969*^9, 3.4954018672609687`*^9}, {
3.4954022872215567`*^9, 3.4954022882115583`*^9}, 3.495488713187342*^9,
3.4954889210576334`*^9, 3.4954892270180616`*^9, 3.4954893399982195`*^9, {
3.4954894833184204`*^9, 3.495489485938424*^9}, 3.4954897194087505`*^9,
3.495493755131653*^9, {3.4954938826158323`*^9, 3.495493884975836*^9},
3.4954939962159915`*^9, {3.4954942766399865`*^9, 3.4954942945800114`*^9},
3.4954948208307486`*^9, {3.495495087335123*^9, 3.495495087705124*^9},
3.4954951805652537`*^9, 3.495495346275087*^9, 3.495495665489626*^9,
3.4954958533919563`*^9, {3.49549609483358*^9, 3.495496110792408*^9},
3.4954961789333277`*^9, 3.495497173544275*^9, {3.495681286888199*^9,
3.4956812892482023`*^9}, {3.5240859566180162`*^9, 3.52408598201486*^9}, {
3.524086057533393*^9, 3.524086058937395*^9}, {3.5242757161181526`*^9,
3.5242757216717625`*^9}, {3.5242763445964565`*^9,
3.5242763477320623`*^9}, {3.5331525961202545`*^9, 3.533152618700286*^9}, {
3.5331527018704023`*^9, 3.5331528058905478`*^9}, {3.533153282981216*^9,
3.5331533342812877`*^9}, {3.533153565251611*^9, 3.533153599281659*^9}, {
3.5332224159616575`*^9, 3.533222435081684*^9}, {3.5332224656717267`*^9,
3.533222494301767*^9}, {3.533223281652869*^9, 3.53322331799292*^9}, {
3.5332234651831264`*^9, 3.5332234684731307`*^9}, {3.533223854473671*^9,
3.5332238609936805`*^9}, {3.5332239572838154`*^9, 3.5332239599938188`*^9},
3.533224847425061*^9, {3.5332249144151554`*^9, 3.533224915905157*^9},
3.533246982034763*^9, 3.5332605459462523`*^9, {3.536350185774555*^9,
3.536350207334585*^9}, {3.5363506584052167`*^9, 3.5363506914352627`*^9}, {
3.5363508662655077`*^9, 3.5363509090255675`*^9}, {3.5363510097557087`*^9,
3.5363510569557743`*^9}, {3.5363512834660916`*^9, 3.536351309536128*^9}, {
3.5363515550764723`*^9, 3.5363516176765594`*^9}, {3.5363516722566357`*^9,
3.5363516724366364`*^9}, {3.536356352083194*^9, 3.536356353383196*^9}, {
3.5363617881968346`*^9, 3.536361833056897*^9}, {3.536366667801671*^9,
3.5363667247217503`*^9}, {3.5363667904918423`*^9, 3.536366799971856*^9}, {
3.536366941382054*^9, 3.536366980882109*^9}, {3.5365968943773336`*^9,
3.536596936123007*^9}, {3.536596976558278*^9, 3.536597025589164*^9},
3.536602461258152*^9, {3.5366940777176437`*^9, 3.5366940881722417`*^9},
3.5366943020244737`*^9, {3.536694516327731*^9, 3.5366945346767807`*^9}, {
3.5369801281282215`*^9, 3.5369801381582355`*^9}, 3.536980329338503*^9, {
3.53698041236862*^9, 3.5369804166186256`*^9}, {3.5369807322990675`*^9,
3.536980746969088*^9}, 3.538444106556738*^9, {3.5384444438259706`*^9,
3.5384444863560305`*^9}, 3.544471282097495*^9, {3.549934369376335*^9,
3.549934370546336*^9}, {3.555274643817338*^9, 3.555274658697359*^9}, {
3.5693429690149527`*^9, 3.569343004485002*^9}, {3.569343115935158*^9,
3.5693431274951744`*^9}, {3.5693438869262376`*^9,
3.5693438923862453`*^9}, {3.5693452399481316`*^9,
3.5693452412481337`*^9}, {3.5693495213494267`*^9,
3.5693495533094716`*^9}, {3.5693499264999943`*^9, 3.569349931960002*^9}, {
3.569351944542819*^9, 3.5693519905128837`*^9}, {3.569352647183803*^9,
3.5693527140438967`*^9}, {3.57488438244142*^9, 3.5748844576015253`*^9}, {
3.6739043440206814`*^9, 3.6739043640248256`*^9}, {3.674084299104566*^9,
3.674084299576593*^9}},
Background->GrayLevel[0.85]],
Cell[BoxData[
RowBox[{
RowBox[{"Int", "[",
RowBox[{
RowBox[{
RowBox[{"u_", "^", "m_."}], "*",
RowBox[{
RowBox[{"Csch", "[", "v_", "]"}], "^", "n_."}]}], ",", "x_Symbol"}],
"]"}], " ", ":=", "\n", " ",
RowBox[{
RowBox[{"Int", "[",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"ExpandToSum", "[",
RowBox[{"u", ",", "x"}], "]"}], "^", "m"}], "*",
RowBox[{
RowBox[{"Csch", "[",
RowBox[{"ExpandToSum", "[",
RowBox[{"v", ",", "x"}], "]"}], "]"}], "^", "n"}]}], ",", "x"}],
"]"}], " ", "/;", "\n",
RowBox[{
RowBox[{"FreeQ", "[",
RowBox[{
RowBox[{"{",
RowBox[{"m", ",", "n"}], "}"}], ",", "x"}], "]"}], " ", "&&", " ",
RowBox[{"LinearQ", "[",
RowBox[{
RowBox[{"{",
RowBox[{"u", ",", "v"}], "}"}], ",", "x"}], "]"}], " ", "&&", " ",
RowBox[{"Not", "[",
RowBox[{"LinearMatchQ", "[",
RowBox[{
RowBox[{"{",
RowBox[{"u", ",", "v"}], "}"}], ",", "x"}], "]"}],
"]"}]}]}]}]], "Code",
CellChangeTimes->{{3.494097165958683*^9, 3.4940971894087152`*^9}, {
3.4940972668388243`*^9, 3.4940972723188314`*^9}, 3.49539148440128*^9,
3.4954018196509027`*^9, {3.495401867050969*^9, 3.4954018672609687`*^9}, {
3.4954022872215567`*^9, 3.4954022882115583`*^9}, 3.495488713187342*^9,
3.4954889210576334`*^9, 3.4954892270180616`*^9, 3.4954893399982195`*^9, {
3.4954894833184204`*^9, 3.495489485938424*^9}, 3.4954897194087505`*^9,
3.495493755131653*^9, {3.4954938826158323`*^9, 3.495493884975836*^9},
3.4954939962159915`*^9, {3.4954942766399865`*^9, 3.4954942945800114`*^9},
3.4954948208307486`*^9, {3.495495087335123*^9, 3.495495087705124*^9},
3.4954951805652537`*^9, 3.495495346275087*^9, 3.495495665489626*^9,
3.4954958533919563`*^9, {3.49549609483358*^9, 3.495496110792408*^9},
3.4954961789333277`*^9, 3.495497173544275*^9, {3.495681286888199*^9,
3.4956812892482023`*^9}, {3.5240859566180162`*^9, 3.52408598201486*^9}, {
3.524086057533393*^9, 3.524086058937395*^9}, {3.5242757161181526`*^9,
3.5242757216717625`*^9}, {3.5242763445964565`*^9,
3.5242763477320623`*^9}, {3.5331525961202545`*^9, 3.533152618700286*^9}, {
3.5331527018704023`*^9, 3.5331528058905478`*^9}, {3.533153282981216*^9,
3.5331533342812877`*^9}, {3.533153565251611*^9, 3.533153599281659*^9}, {
3.5332224159616575`*^9, 3.533222435081684*^9}, {3.5332224656717267`*^9,
3.533222494301767*^9}, {3.533223281652869*^9, 3.53322331799292*^9}, {
3.5332234651831264`*^9, 3.5332234684731307`*^9}, {3.533223854473671*^9,
3.5332238609936805`*^9}, {3.5332239572838154`*^9, 3.5332239599938188`*^9},
3.533224847425061*^9, {3.5332249144151554`*^9, 3.533224915905157*^9},
3.533246982034763*^9, 3.5332605459462523`*^9, {3.536350185774555*^9,
3.536350207334585*^9}, {3.5363506584052167`*^9, 3.5363506914352627`*^9}, {
3.5363508662655077`*^9, 3.5363509090255675`*^9}, {3.5363510097557087`*^9,
3.5363510569557743`*^9}, {3.5363512834660916`*^9, 3.536351309536128*^9}, {
3.5363515550764723`*^9, 3.5363516176765594`*^9}, {3.5363516722566357`*^9,
3.5363516724366364`*^9}, {3.536356352083194*^9, 3.536356353383196*^9}, {
3.5363617881968346`*^9, 3.536361833056897*^9}, {3.536366667801671*^9,
3.5363667247217503`*^9}, {3.5363667904918423`*^9, 3.536366799971856*^9}, {
3.536366941382054*^9, 3.536366980882109*^9}, {3.5365968943773336`*^9,
3.536596936123007*^9}, {3.536596976558278*^9, 3.536597025589164*^9},
3.536602461258152*^9, {3.5366940777176437`*^9, 3.5366940881722417`*^9},
3.5366943020244737`*^9, {3.536694516327731*^9, 3.5366945346767807`*^9}, {
3.5369801281282215`*^9, 3.5369801381582355`*^9}, 3.536980329338503*^9, {
3.53698041236862*^9, 3.5369804166186256`*^9}, {3.5369807322990675`*^9,
3.536980746969088*^9}, 3.538444106556738*^9, {3.5384444438259706`*^9,
3.5384444863560305`*^9}, 3.544471282097495*^9, {3.549934369376335*^9,
3.549934370546336*^9}, {3.555274643817338*^9, 3.555274658697359*^9}, {
3.5693429690149527`*^9, 3.569343004485002*^9}, {3.569343115935158*^9,
3.5693431274951744`*^9}, {3.5693438869262376`*^9,
3.5693438923862453`*^9}, {3.5693452399481316`*^9,
3.5693452412481337`*^9}, {3.5693495213494267`*^9,
3.5693495533094716`*^9}, {3.5693499264999943`*^9, 3.569349931960002*^9}, {
3.569351944542819*^9, 3.5693519905128837`*^9}, {3.569352647183803*^9,
3.5693527140438967`*^9}, {3.57488438244142*^9, 3.5748844576015253`*^9}, {
3.6739043440206814`*^9, 3.673904397521742*^9}, {3.6740843082780905`*^9,
3.674084310124196*^9}},
Background->GrayLevel[0.85]],
Cell["", "Subsubsection",
CellDingbat->None,
CellChangeTimes->{
3.4796643211106243`*^9, {3.536351324436149*^9, 3.536351326496152*^9}, {
3.5363515481064625`*^9, 3.536351548866463*^9}}]
}, Closed]]
},
AutoGeneratedPackage->Automatic,
CellGrouping->Manual,
WindowSize->{1912, 961},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
PrintingCopies->1,
PrintingStartingPageNumber->1,
PrintingPageRange->{1, 32000},
PageHeaders->{{
Cell[
TextData[{
StyleBox[
CounterBox["Page"], "PageNumber"], " ", "|", " ",
StyleBox[
ValueBox["FileName"], "Header"]}], "Header",
CellMargins -> {{0, Inherited}, {Inherited, Inherited}}], None, None}, {
Cell[
TextData[{
"Rules", " ", "for", " ", "integrands", " ", "of", " ", "the", " ",
"form", " ", "(", "c", "+", "d", " ", "x", ")", "^", "m", " ", "(", "a",
"+", "b", " ", "sech", "(", "c", "+", "d", " ", "x", ")", ")", "^",
"n"}], "Header",
CellMargins -> {{0, Inherited}, {Inherited, Inherited}}], None,
Cell[
TextData[
CounterBox["Page", CounterFunction :> Identity]], "Header",
CellMargins -> {{Inherited, 0}, {Inherited, Inherited}}]}},
PageFooters->{{None, None, None}, {None, None, None}},
PageHeaderLines->{False, False},
PageFooterLines->{False, False},
PrintingOptions->{"FacingPages"->False,
"FirstPageFace"->Right,
"FirstPageFooter"->False,
"FirstPageHeader"->False,
"Magnification"->1.,
"PaperOrientation"->"Landscape",
"PaperSize"->{783., 601.8},
"PrintCellBrackets"->False,
"PrintMultipleHorizontalPages"->False,
"PrintRegistrationMarks"->False,
"PrintingMargins"->28.8},
Magnification->1.399999976158142,
FrontEndVersion->"8.0 for Microsoft Windows (64-bit) (October 6, 2011)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[545, 20, 2235, 43, 42, "Subsubtitle"],
Cell[CellGroupData[{
Cell[2805, 67, 5374, 89, 53, "Subsubtitle"],
Cell[8182, 158, 448, 6, 48, "Subsubsection"],
Cell[8633, 166, 2759, 45, 36, "Subsubsection"],
Cell[11395, 213, 3179, 56, 74, "Subsubtitle"],
Cell[14577, 271, 771, 11, 48, "Subsubsection"],
Cell[15351, 284, 4647, 85, 145, "Code"],
Cell[20001, 371, 4647, 85, 159, "Code"],
Cell[24651, 458, 190, 4, 48, "Subsubsection"]
}, Closed]]
}
]
*)
(* End of internal cache information *)