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algebrite/tests/integral.coffee

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1test_integral = ->
run_test [
3
"clearall",
"",
6
"tty=1",
"",
9
"integral(x^2+x)-(1/2*x^2+1/3*x^3)",
"0",
12
#1
"integral(A,X)",
"A*X",
16
#4
"integral(A+B,X)-(A*X+B*X)",
"0",
20
#9
"integral(1/X,X)",
"log(X)",
24
#11
"integral(exp(X),X)",
"exp(X)",
28
#12
"integral(exp(A*X),X)-exp(A*X)/A",
"0",
32
#14
"integral(log(X),X)-X*log(X)+X",
"0",
36
#15
"integral(3^X*log(3),X)",
"3^X",
40
#16
"integral(1/(3+x^2),x)-3^(-1/2)*arctan(3^(-1/2)*x)",
"0",
44
#17
"integral(1/(a-x^2),x)-a^(-1/2)*arctanh(a^(-1/2)*x)",
"0",
48
#19
"integral(1/sqrt(a-x^2),x)-arcsin(a^(-1/2)*x)",
"0",
52
#20
"integral(1/sqrt(a+x^2),x)-(log(x+(a+x^2)^(1/2)))",
"0",
56
#27
"integral(1/(a+b*x),x)-(log(a+b*x)/b)",
"0",
60
#28
"integral(1/(A+B*X)^2,X)+1/B*1/(A+B*X)",
"0",
64
#29
"integral(1/(a+b*x)^3,x)+1/2*1/b*(a+b*x)^(-2)",
"0",
68
#30
"integral(X/(A+B*X),X)+A*B^(-2)*log(A+B*X)-X/B",
"0",
72
#31
"integral(X/(A+B*X)^2,X)-1/B^2*(log(A+B*X)+A/(A+B*X))",
"0",
76
#33
"integral(X^2/(A+B*X),X)-1/B^2*(1/2*(A+B*X)^2-2*A*(A+B*X)+A^2*log(A+B*X))",
"0",
80
#34
"integral(X^2/(A+B*X)^2,X)-1/B^3*(A+B*X-2*A*log(A+B*X)-A^2/(A+B*X))",
"0",
84
#35
"integral(X^2/(A+B*X)^3,X)-1/B^3*(log(A+B*X)+2*A/(A+B*X)-1/2*A^2/(A+B*X)^2)",
"0",
88
#37
"integral(1/X*1/(A+B*X),X)+1/A*log((A+B*X)/X)",
"0",
92
#38
"integral(1/X*1/(A+B*X)^2,X)-1/A*1/(A+B*X)+1/A^2*log((A+B*X)/X)",
"0",
96
#39
"integral(1/X*1/(A+B*X)^3,X)-1/A^3*(1/2*((2*A+B*X)/(A+B*X))^2+log(X/(A+B*X)))",
"0",
100
#40
"integral(1/X^2*1/(A+B*X),X)+1/(A*X)-B/A^2*log((A+B*X)/X)",
"0",
104
#41
"integral(1/X^3*1/(A+B*X),X)-(2*B*X-A)/(2*A^2*X^2)-B^2/A^3*log(X/(A+B*X))",
"0",
108
#42
"integral(1/X^2*1/(A+B*X)^2,X)+(A+2*B*X)/(A^2*X*(A+B*X))-2*B/A^3*log((A+B*X)/X)",
"0",
112
#60
"integral(1/(2+3*X^2),X)-1/sqrt(6)*arctan(1/2*X*sqrt(6))",
"0",
"integral(1/(-2-3*X^2),X)-1/sqrt(6)*arctan(-1/2*X*sqrt(6))",
"0",
118
#61
"integral(1/(2-3*X^2),X)-1/2*1/sqrt(6)*log((2+X*sqrt(6))/(2-X*sqrt(6)))",
"0",
"integral(1/(-2+3*X^2),X)-1/2*1/sqrt(6)*log((-2+X*sqrt(6))/(-2-X*sqrt(6)))",
"0",
124
#63
"integral(X/(A+B*X^2),X)-1/2*1/B*log(A+B*X^2)",
"0",
128
#64
"integral(X^2/(A+B*X^2),X)-X/B+A/B*integral(1/(A+B*X^2),X)",
"0",
132
#65
"integral(1/(A+B*X^2)^2,X)-X/(2*A*(A+B*X^2))-1/2*1/A*integral(1/(A+B*X^2),X)",
"0",
136
#70
"integral(1/X*1/(A+B*X^2),X)-1/2*1/A*log(X^2/(A+B*X^2))",
"0",
140
#71
"integral(1/X^2*1/(A+B*X^2),X)+1/(A*X)+B/A*integral(1/(A+B*X^2),X)",
"0",
144
#74
"integral(1/(A+B*X^3),X)-1/3*1/A*(A/B)^(1/3)*(1/2*log(((A/B)^(1/3)+X)^3/(A+B*X^3))+sqrt(3)*arctan((2*X-(A/B)^(1/3))*(A/B)^(-1/3)/sqrt(3)))",
"0",
148
#76
"integral(X^2/(A+B*X^3),X)-1/3*1/B*log(A+B*X^3)",
"0",
152
# commenting this out because the definite integral of this one
# between 0 and pi was incorrect AND the indefinite integral
# became incorrect after I avoided having roots in the denominator
# when doing multiplications. The two things combined made me
# think to eliminate this test.
#77
#"integral(1/(2+3*X^4),X)-1/2*1/2*(2/3/4)^(1/4)*(1/2*log((X^2+2*(2/3/4)^(1/4)*X+2*(2/3/4)^(1/2))/(X^2-2*(2/3/4)^(1/4)*X+2*(2/3/4)^(1/2)))+arctan(2*(2/3/4)^(1/4)*X/(2*(2/3/4)^(1/2)-X^2)))",
#"0",
161
# commenting this out because the definite integral of this one
# between 0 and pi was incorrect AND the indefinite integral
# became incorrect after I avoided having roots in the denominator
# when doing multiplications. The two things combined made me
# think to eliminate this test.
#78
#"integral(1/(2-3*X^4),X)-1/2*(2/3)^(1/4)/2*(1/2*log((X+(2/3)^(1/4))/(X-(2/3)^(1/4)))+arctan(X*(2/3)^(-1/4)))",
#"0",
170
#79
"integral(X/(2+3*X^4),X)-1/2*1/3*1/sqrt(2/3)*arctan(X^2/sqrt(2/3))",
"0",
174
#80
"integral(X/(2-3*X^4),X)+1/4*1/3*sqrt(3/2)*log((X^2-sqrt(2/3))/(X^2+sqrt(2/3)))",
"0",
178
# commenting this out because the definite integral of this one
# between 0 and pi was incorrect AND the indefinite integral
# became incorrect after I avoided having roots in the denominator
# when doing multiplications. The two things combined made me
# think to eliminate this test.
#81
#"integral(X^2/(2+3*X^4),X)-1/4*1/3*(2/3/4)^(-1/4)*(1/2*log((X^2-2*(2/3/4)^(1/4)*X+2*sqrt(2/3/4))/(X^2+2*(2/3/4)^(1/4)*X+2*sqrt(2/3/4)))+arctan(2*(2/3/4)^(1/4)*X/(2*sqrt(2/3/4)-X^2)))",
#"0",
187
# commenting this out because the definite integral of this one
# between 0 and pi was incorrect AND the indefinite integral
# became incorrect after I avoided having roots in the denominator
# when doing multiplications. The two things combined made me
# think to eliminate this test.
#82
#"integral(X^2/(2-3*X^4),X)+1/4*1/3*(2/3)^(-1/4)*(log((X-(2/3)^(1/4))/(X+(2/3)^(1/4)))+2*arctan(X*(2/3)^(-1/4)))",
#"0",
196
#83
"integral(X^3/(A+B*X^4),X)-1/4*1/B*log(A+B*X^4)",
"0",
200
#124
"integral(sqrt(A+B*X),X)-2/3/B*sqrt((A+B*X)^3)",
"0",
204
#125
"integral(X*sqrt(A+B*X),X)+2*(2*A-3*B*X)*sqrt((A+B*X)^3)/15*B^(-2)",
"0",
208
#126
"integral(X^2*sqrt(A+B*X),X)-2*(8*A^2-12*A*B*X+15*B^2*X^2)*sqrt((A+B*X)^3)/105*B^(-3)",
"0",
212
#128
"integral(sqrt(A+B*X)/X,X)-2*sqrt(A+B*X)-A*integral(1/X*1/sqrt(A+B*X),X)",
"0",
216
#129
"integral(sqrt(A+B*X)/X^2,X)+sqrt(A+B*X)/X-B/2*integral(1/X*1/sqrt(A+B*X),X)",
"0",
220
#131
"integral(1/sqrt(A+B*X),X)-2*sqrt(A+B*X)/B",
"0",
224
#132
"integral(X/sqrt(A+B*X),X)+2/3*(2*A-B*X)*sqrt(A+B*X)/B^2",
"0",
228
#133
"integral(X^2/sqrt(A+B*X),X)-2/15*(8*A^2-4*A*B*X+3*B^2*X^2)*sqrt(A+B*X)/B^3",
"0",
232
#134
"integral(1/X*1/sqrt(2+B*X),X)-1/sqrt(2)*log((sqrt(2+B*X)-sqrt(2))/(sqrt(2+B*X)+sqrt(2)))",
"0",
236
#136
"integral(1/X*1/sqrt(-2+B*X),X)-2/sqrt(2)*arctan(sqrt((-2+B*X)/2))",
"0",
240
#137
"integral(1/X^2*1/sqrt(A+B*X),X)+sqrt(A+B*X)/A/X+1/2*B/A*integral(1/X*1/sqrt(A+B*X),X)",
"0",
244
#156
"integral(sqrt(X^2+A),X)-1/2*(X*sqrt(X^2+A)+A*log(X+sqrt(X^2+A)))",
"0",
248
#157
"integral(1/sqrt(X^2+A),X)-log(X+sqrt(X^2+A))",
"0",
252
#158
"integral(1/X*1/sqrt(X^2-2),X)-arcsec(X/sqrt(2))/sqrt(2)",
"0",
256
#159
"integral(1/X*1/sqrt(X^2+2),X)+1/sqrt(2)*log((sqrt(2)+sqrt(X^2+2))/X)",
"0",
260
#160
"integral(sqrt(X^2+2)/X,X)-sqrt(X^2+2)+sqrt(2)*log((sqrt(2)+sqrt(X^2+2))/X)",
"0",
264
#161
"integral(sqrt(X^2-2)/X,X)-sqrt(X^2-2)+sqrt(2)*arcsec(X/sqrt(2))",
"0",
268
#162
"integral(X/sqrt(X^2+A),X)-sqrt(X^2+A)",
"0",
272
#163
"integral(X*sqrt(X^2+A),X)-1/3*sqrt((X^2+A)^3)",
"0",
276
#164 fails after Jan 2017 changes to abs/mag
#"integral(sqrt((X^2+A)^3),X)-1/4*(X*sqrt((X^2+A)^3)+3/2*A*X*sqrt(X^2+A)+3/2*A^2*log(X+sqrt(X^2+A)))",
#"0",
280
#"integral(sqrt((X^2-A)^3),X)-1/4*(X*sqrt((X^2-A)^3)-3/2*A*X*sqrt(X^2-A)+3/2*A^2*log(X+sqrt(X^2-A)))",
#"0",
283
#165 fails after Jan 2017 changes to abs/mag
#"integral(1/sqrt((X^2+A)^3),X)-X/A/sqrt(X^2+A)",
#"0",
287
#166 fails after Jan 2017 changes to abs/mag
#"integral(X/sqrt((X^2+A)^3),X)+1/sqrt(X^2+A)",
#"0",
291
#167 fails after Jan 2017 changes to abs/mag
#"integral(X*sqrt((X^2+A)^3),X)-1/5*sqrt((X^2+A)^5)",
#"0",
295
#168
"integral(X^2*sqrt(X^2+A),X)-1/4*X*sqrt((X^2+A)^3)+1/8*A*X*sqrt(X^2+A)+1/8*A^2*log(X+sqrt(X^2+A))",
"0",
299
#169
"integral(X^3*sqrt(X^2+7),X)-(1/5*X^2-2/15*7)*sqrt((X^2+7)^3)",
"0",
303
#170
"integral(X^3*sqrt(X^2-7),X)-(sqrt((X^2-7)^5)/5+7*sqrt((X^2-7)^3)/3)",
"0",
307
#171
"integral(X^2/sqrt(X^2+A),X)-1/2*X*sqrt(X^2+A)+1/2*A*log(X+sqrt(X^2+A))",
"0",
311
#172
"integral(X^3/sqrt(X^2+A),X)-1/3*sqrt((X^2+A)^3)+A*sqrt(X^2+A)",
"0",
315
#173
"integral(1/X^2*1/sqrt(X^2+A),X)+sqrt(X^2+A)/A/X",
"0",
319
#174
"integral(1/X^3*1/sqrt(X^2+2),X)+1/2*sqrt(X^2+2)/2/X^2-1/2*log((sqrt(2)+sqrt(X^2+2))/X)/(sqrt(2)^3)",
"0",
323
#175
"integral(1/X^3*1/sqrt(X^2-2),X)-1/2*sqrt(X^2-2)/2/X^2-1/2*1/(2^(3/2))*arcsec(X/(2^(1/2)))",
"0",
327
#176+
"integral(X^2*sqrt((X^2+2^2)^3),X)\
-1/6*X*sqrt((X^2+2^2)^5)\
+1/24*(2^2)*X*sqrt((X^2+2^2)^3)\
+1/16*(2^4)X*sqrt(X^2+2^2)\
+1/16*(2^6)*log(X+sqrt(X^2+2^2))",
"0",
335
#176-
"integral(X^2*sqrt((X^2-2^2)^3),X)\
-1/6*X*sqrt((X^2-2^2)^5)\
-1/24*(2^2)*X*sqrt((X^2-2^2)^3)\
+1/16*(2^4)X*sqrt(X^2-2^2)\
-1/16*(2^6)*log(X+sqrt(X^2-2^2))",
"0",
343
#177+
"integral(X^3*sqrt((X^2+7^2)^3),X)\
-1/7*sqrt((X^2+7^2)^7)\
+1/5*(7^2)*sqrt((X^2+7^2)^5)",
"0",
349
#177-
"integral(X^3*sqrt((X^2-7^2)^3),X)\
-1/7*sqrt((X^2-7^2)^7)\
-1/5*(7^2)*sqrt((X^2-7^2)^5)",
"0",
355
#196
"simplify(integral(1/(X-A)/sqrt(X^2-A^2),X)+sqrt(X^2-A^2)/A/(X-A))",
"0",
"simplify(1/(X-A)/sqrt(X^2-A^2)-d(integral(1/(X-A)/sqrt(X^2-A^2),X),X))",
"0",
361
#197
"integral(1/(X+A)/sqrt(X^2-A^2),X)-sqrt(X^2-A^2)/A/(X+A)",
"0",
"simplify(1/(X+A)/sqrt(X^2-A^2)-d(integral(1/(X+A)/sqrt(X^2-A^2),X),X))",
"0",
367
#200
"integral(sqrt(7-X^2),X)-1/2*(X*sqrt(7-X^2)+7*arcsin(X/sqrt(7)))",
"0",
371
#201
"integral(1/sqrt(7-X^2),X)-arcsin(X/sqrt(7))",
"0",
375
#202
"integral(1/X*1/sqrt(7-X^2),X)+1/sqrt(7)*log((sqrt(7)+sqrt(7-X^2))/X)",
"0",
379
#203
"integral(sqrt(7-X^2)/X,X)\
-sqrt(7-X^2)+sqrt(7)*log((sqrt(7)+sqrt(7-X^2))/X)",
"0",
384
#204
"integral(X/sqrt(A-X^2),X)\
+sqrt(A-X^2)",
"0",
389
#205
"integral(X*sqrt(A-X^2),X)\
+1/3*sqrt((A-X^2)^3)",
"0",
394
#210
"integral(X^2*sqrt(7-X^2),X)\
+1/4*X*sqrt((7-X^2)^3)\
-7/8*(X*sqrt(7-X^2)+7*arcsin(X/sqrt(7)))",
"0",
400
#211
"integral(X^3*sqrt(7-X^2),X)\
-(-1/5*X^2-2/15*7)*sqrt((7-X^2)^3)",
"0",
405
#214
"integral(X^2/sqrt(7-X^2),X)\
+X/2*sqrt(7-X^2)\
-7/2*arcsin(X/sqrt(7))",
"0",
411
#215
"integral(1/X^2*1/sqrt(7-X^2),X)\
+sqrt(7-X^2)/7/X",
"0",
416
#216
"integral(sqrt(7-X^2)/X^2,X)\
+sqrt(7-X^2)/X\
+arcsin(X/sqrt(7))",
"0",
422
#217
"integral(sqrt(7-X^2)/X^3,X)\
+1/2*sqrt(7-X^2)/X^2\
-1/2*log((sqrt(7)+sqrt(7-X^2))/X)/sqrt(7)",
"0",
428
#218
"integral(sqrt(7-X^2)/X^4,X)\
+1/3*sqrt((7-X^2)^3)/7/X^3",
"0",
433
#273
"integral(sqrt(7*X^2+C),X)-X*sqrt(7*X^2+C)/2-C*log(X*sqrt(7)+sqrt(7*X^2+C))/2/sqrt(7)",
"0",
437
#274
"integral(sqrt(-7*X^2+C),X)-X*sqrt(-7*X^2+C)/2-C*arcsin(X*sqrt(7/C))/2/sqrt(7)",
"0",
441
#290
"integral(sin(A*X),X)+cos(A*X)/A",
"0",
445
#291
"integral(cos(A*X),X)-sin(A*X)/A",
"0",
449
#292
"integral(tan(A*X),X)+log(cos(A*X))/A",
"0",
453
#293
"integral(1/tan(A*X),X)-log(sin(A*X))/A",
"0",
457
#294
"integral(1/cos(A*X),X)-log(tan(pi/4+A*X/2))/A",
"0",
461
#295
"integral(1/sin(A*X),X)-log(tan(A*X/2))/A",
"0",
465
#296
"integral(sin(A*X)^2,X)-X/2+sin(2*A*X)/(4*A)",
"0",
469
#297
"integral(sin(A*X)^3,X)+cos(A*X)*(sin(A*X)^2+2)/(3*A)",
"0",
473
#298
"integral(sin(A*X)^4,X)-3/8*X+sin(2*A*X)/(4*A)-sin(4*A*X)/(32*A)",
"0",
477
#302
"integral(cos(A*X)^2,X)-X/2-sin(2*A*X)/(4*A)",
"0",
481
#303
"integral(cos(A*X)^3,X)-sin(A*X)*(cos(A*X)^2+2)/(3*A)",
"0",
485
#304
"integral(cos(A*X)^4,X)-3/8*X-sin(2*A*X)/(4*A)-sin(4*A*X)/(32*A)",
"0",
489
#308
"integral((1/sin(A*X))^2,X)+1/A*1/tan(A*X)",
"0",
493
#312
"integral((1/cos(A*X))^2,X)-tan(A*X)/A",
"0",
497
#318
"integral(sin(A*X)*cos(A*X),X)-sin(A*X)^2/(2*A)",
"0",
501
#320
"integral(sin(A*X)^2*cos(A*X)^2,X)+sin(4*A*X)/(32*A)-X/8",
"0",
505
#326
"integral(sin(A*X)/cos(A*X)/cos(A*X),X)-1/(A*cos(A*X))",
"0",
509
#327
"integral(sin(A*X)^2/cos(A*X),X)+sin(A*X)/A-log(tan(pi/4+A*X/2))/A",
"0",
513
#328
"integral(cos(A*X)/sin(A*X)^2,X)+1/(A*sin(A*X))",
"0",
517
#329
"integral(1/sin(A*X)/cos(A*X),X)-log(tan(A*X))/A",
"0",
521
#330
"integral(1/sin(A*X)/cos(A*X)^2,X)-(1/cos(A*X)+log(tan(A*X/2)))/A",
"0",
525
#332
"integral(1/sin(A*X)^2/cos(A*X),X)-(log(tan(pi/4+A*X/2))-1/sin(A*X))/A",
"0",
529
#333
"integral(1/sin(A*X)^2/cos(A*X)^2,X)+2/(A*tan(2*A*X))",
"0",
533
#335
"integral(sin(A+B*X),X)+cos(A+B*X)/B",
"0",
537
#336
"integral(cos(A+B*X),X)-sin(A+B*X)/B",
"0",
541
#337+
"integral(1/(1+sin(A*X)),X)+tan(pi/4-A*X/2)/A",
"0",
545
#337b+
"integral(1/(B+B*sin(A*X)),X)+tan(pi/4-A*X/2)/A/B",
"0",
549
#337-
"integral(1/(1-sin(A*X)),X)-tan(pi/4+A*X/2)/A",
"0",
553
#337b-
"integral(1/(B-B*sin(A*X)),X)-tan(pi/4+A*X/2)/A/B",
"0",
557
#338
"integral(1/(1+cos(A*X)),X)-tan(A*X/2)/A",
"0",
561
#339
"integral(1/(1-cos(A*X)),X)+1/(A*tan(A*X/2))",
"0",
565
#340
"integral(1/(A+B*sin(X)),X)-1/sqrt(B^2-A^2)*log((A*tan(X/2)+B-sqrt(B^2-A^2))/(A*tan(X/2)+B+sqrt(B^2-A^2)))",
"0",
569
#341
"integral(1/(A+B*cos(X)),X)-1/sqrt(B^2-A^2)*log((sqrt(B^2-A^2)*tan(X/2)+A+B)/(sqrt(B^2-A^2)*tan(X/2)-A-B))",
"0",
573
#389
"x*sin(A*x)-d(integral(x*sin(A*x)))",
"0",
577
#390
"x^2*sin(A*x)-d(integral(x^2*sin(A*x)))",
"0",
581
#393
"x*cos(A*x)-d(integral(x*cos(A*x)))",
"0",
585
#394
"x^2*cos(A*x)-d(integral(x^2*cos(A*x)))",
"0",
589
#441
"integral(arcsin(A*X),X)-X*arcsin(A*X)-sqrt(1-A^2*X^2)/A",
"0",
593
#442
"integral(arccos(A*X),X)-X*arccos(A*X)+sqrt(1-A^2*X^2)/A",
"0",
597
#443
"integral(arctan(A*X),X)-X*arctan(A*X)+log(1+A^2*X^2)/(2*A)",
"0",
601
#485
"integral(log(X),X)-X*log(X)+X",
"0",
605
#485a
"integral(log(A*X),X)-X*log(A*X)+X",
"0",
609
#486
"integral(X*log(X),X)-1/2*X^2*log(X)+1/4*X^2",
"0",
613
#486a
"integral(X*log(A*X),X)-1/2*X^2*log(A*X)+1/4*X^2",
"0",
617
#487
"integral(X^2*log(A*X),X)-1/3*X^3*log(A*X)+X^3/9",
"0",
621
#489
"integral(log(X)^2,X)-X*log(X)^2+2*X*log(X)-2*X",
"0",
625
#493
"integral(1/X*1/log(A*X),X)-log(log(A*X))",
"0",
629
#499
"integral(log(A*X+B),X)-(A*X+B)*log(A*X+B)/A+X",
"0",
633
#500
"integral(log(A*X+B)/X^2,X)-A*log(X)/B+(A*X+B)*log(A*X+B)/B/X",
"0",
637
#554
"integral(sinh(X),X)-cosh(X)",
"0",
641
#555
"integral(cosh(X),X)-sinh(X)",
"0",
645
#556
"integral(tanh(X),X)-log(cosh(X))",
"0",
649
#560
"integral(X*sinh(X),X)-X*cosh(X)+sinh(X)",
"0",
653
#562
"integral(X*cosh(X),X)-X*sinh(X)+cosh(X)",
"0",
657
#566
"integral(sinh(X)^2,X)-sinh(2*X)/4+X/2",
"0",
661
#569
"integral(tanh(X)^2,X)-X+tanh(X)",
"0",
665
#572
"integral(cosh(X)^2,X)-sinh(2*X)/4-X/2",
"0",
669
# test integral(exp(a*x^2))
671
"integral(exp(a*x^2))+i*sqrt(pi)*erf(i*sqrt(a)*x)/sqrt(a)/2",
"0",
674
"integral(exp(-x^2))-sqrt(pi)*erf(x)/2",
"0",
677
# before abs/mag changes of Jan 2017
# this integral gave the more compact result of:
#   sqrt(pi/3)*erf(sqrt(3)*x)/2
# but the new given one is still correct
"integral(exp(-3*x^2))-pi^(1/2)*erf(3^(1/2)*x)/(2*3^(1/2))",
"0",
684
"integral(1/x*1/(a+log(x)),x)-log(a+log(x))",
"0",
687
"integral(exp(a*x+b*x))",
"exp((a+b)*x)/(a+b)",
690
"integral(x*exp(a*x))",
"-exp(a*x)/(a^2)+x*exp(a*x)/a",
"derivative",
"x*exp(a*x)",
695
"integral(x*exp(a*x+b))",
"-exp(a*x+b)/(a^2)+x*exp(a*x+b)/a",
"derivative",
"x*exp(a*x+b)",
700
"integral(x*exp(-a*x+b))",
"-exp(-a*x+b)/(a^2)-x*exp(-a*x+b)/a",
"derivative",
"x*exp(-a*x+b)",
705
"integral(x^2*exp(a*x))",
"2*exp(a*x)/(a^3)-2*x*exp(a*x)/(a^2)+x^2*exp(a*x)/a",
"derivative",
"x^2*exp(a*x)",
710
"integral(x^2*exp(a*x+b))",
"2*exp(a*x+b)/(a^3)-2*x*exp(a*x+b)/(a^2)+x^2*exp(a*x+b)/a",
"derivative",
"x^2*exp(a*x+b)",
715
"integral(x^3*exp(a*x))",
"-6*exp(a*x)/(a^4)+6*x*exp(a*x)/(a^3)-3*x^2*exp(a*x)/(a^2)+x^3*exp(a*x)/a",
"derivative",
"x^3*exp(a*x)",
720
"integral(x^3*exp(a*x+b))",
"-6*exp(a*x+b)/(a^4)+6*x*exp(a*x+b)/(a^3)-3*x^2*exp(a*x+b)/(a^2)+x^3*exp(a*x+b)/a",
"derivative",
"x^3*exp(a*x+b)",
725
# here
"integral(sqrt(a*x^2+b))",
"Stop: integral: sorry, could not find a solution",
729
"integral(x^2*(1-x^2)^(3/2))-(x*sqrt(1-x^2)*(-8*x^4+14*x^2-3)+3*arcsin(x))/48",
"0",
732
"integral(x^4*(1-x^2)^(3/2))-(-x*sqrt(1-x^2)*(16*x^6-24*x^4+2*x^2+3)+3*arcsin(x))/128",
"0",
735
"integral(x^2*(1-x^2)^(5/2))-(x*sqrt(1-x^2)*(48*x^6-136*x^4+118*x^2-15)+15*arcsin(x))/384",
"0",
]

1	`test_integral = ->`
2	`run_test [`
3
4	`"clearall",`
5	`"",`
6
7	`"tty=1",`
8	`"",`
9
10	`"integral(x^2+x)-(1/2x^2+1/3x^3)",`
11	`"0",`
12
13	`#1`
14	`"integral(A,X)",`
15	`"A*X",`
16
17	`#4`
18	`"integral(A+B,X)-(AX+BX)",`
19	`"0",`
20
21	`#9`
22	`"integral(1/X,X)",`
23	`"log(X)",`
24
25	`#11`
26	`"integral(exp(X),X)",`
27	`"exp(X)",`
28
29	`#12`
30	`"integral(exp(AX),X)-exp(AX)/A",`
31	`"0",`
32
33	`#14`
34	`"integral(log(X),X)-X*log(X)+X",`
35	`"0",`
36
37	`#15`
38	`"integral(3^X*log(3),X)",`
39	`"3^X",`
40
41	`#16`
42	`"integral(1/(3+x^2),x)-3^(-1/2)arctan(3^(-1/2)x)",`
43	`"0",`
44
45	`#17`
46	`"integral(1/(a-x^2),x)-a^(-1/2)arctanh(a^(-1/2)x)",`
47	`"0",`
48
49	`#19`
50	`"integral(1/sqrt(a-x^2),x)-arcsin(a^(-1/2)*x)",`
51	`"0",`
52
53	`#20`
54	`"integral(1/sqrt(a+x^2),x)-(log(x+(a+x^2)^(1/2)))",`
55	`"0",`
56
57	`#27`
58	`"integral(1/(a+bx),x)-(log(a+bx)/b)",`
59	`"0",`
60
61	`#28`
62	`"integral(1/(A+BX)^2,X)+1/B1/(A+B*X)",`
63	`"0",`
64
65	`#29`
66	`"integral(1/(a+bx)^3,x)+1/21/b(a+bx)^(-2)",`
67	`"0",`
68
69	`#30`
70	`"integral(X/(A+BX),X)+AB^(-2)log(A+BX)-X/B",`
71	`"0",`
72
73	`#31`
74	`"integral(X/(A+BX)^2,X)-1/B^2(log(A+BX)+A/(A+BX))",`
75	`"0",`
76
77	`#33`
78	`"integral(X^2/(A+BX),X)-1/B^2(1/2(A+BX)^2-2A(A+BX)+A^2log(A+B*X))",`
79	`"0",`
80
81	`#34`
82	`"integral(X^2/(A+BX)^2,X)-1/B^3(A+BX-2Alog(A+BX)-A^2/(A+B*X))",`
83	`"0",`
84
85	`#35`
86	`"integral(X^2/(A+BX)^3,X)-1/B^3(log(A+BX)+2A/(A+BX)-1/2A^2/(A+B*X)^2)",`
87	`"0",`
88
89	`#37`
90	`"integral(1/X1/(A+BX),X)+1/Alog((A+BX)/X)",`
91	`"0",`
92
93	`#38`
94	`"integral(1/X1/(A+BX)^2,X)-1/A1/(A+BX)+1/A^2log((A+BX)/X)",`
95	`"0",`
96
97	`#39`
98	`"integral(1/X1/(A+BX)^3,X)-1/A^3(1/2((2A+BX)/(A+BX))^2+log(X/(A+BX)))",`
99	`"0",`
100
101	`#40`
102	`"integral(1/X^21/(A+BX),X)+1/(AX)-B/A^2log((A+B*X)/X)",`
103	`"0",`
104
105	`#41`
106	`"integral(1/X^31/(A+BX),X)-(2BX-A)/(2A^2X^2)-B^2/A^3log(X/(A+BX))",`
107	`"0",`
108
109	`#42`
110	`"integral(1/X^21/(A+BX)^2,X)+(A+2BX)/(A^2X(A+BX))-2B/A^3log((A+BX)/X)",`
111	`"0",`
112
113	`#60`
114	`"integral(1/(2+3X^2),X)-1/sqrt(6)arctan(1/2Xsqrt(6))",`
115	`"0",`
116	`"integral(1/(-2-3X^2),X)-1/sqrt(6)arctan(-1/2Xsqrt(6))",`
117	`"0",`
118
119	`#61`
120	`"integral(1/(2-3X^2),X)-1/21/sqrt(6)log((2+Xsqrt(6))/(2-X*sqrt(6)))",`
121	`"0",`
122	`"integral(1/(-2+3X^2),X)-1/21/sqrt(6)log((-2+Xsqrt(6))/(-2-X*sqrt(6)))",`
123	`"0",`
124
125	`#63`
126	`"integral(X/(A+BX^2),X)-1/21/Blog(A+BX^2)",`
127	`"0",`
128
129	`#64`
130	`"integral(X^2/(A+BX^2),X)-X/B+A/Bintegral(1/(A+B*X^2),X)",`
131	`"0",`
132
133	`#65`
134	`"integral(1/(A+BX^2)^2,X)-X/(2A(A+BX^2))-1/21/Aintegral(1/(A+B*X^2),X)",`
135	`"0",`
136
137	`#70`
138	`"integral(1/X1/(A+BX^2),X)-1/21/Alog(X^2/(A+B*X^2))",`
139	`"0",`
140
141	`#71`
142	`"integral(1/X^21/(A+BX^2),X)+1/(AX)+B/Aintegral(1/(A+B*X^2),X)",`
143	`"0",`
144
145	`#74`
146	`"integral(1/(A+BX^3),X)-1/31/A(A/B)^(1/3)(1/2log(((A/B)^(1/3)+X)^3/(A+BX^3))+sqrt(3)arctan((2X-(A/B)^(1/3))*(A/B)^(-1/3)/sqrt(3)))",`
147	`"0",`
148
149	`#76`
150	`"integral(X^2/(A+BX^3),X)-1/31/Blog(A+BX^3)",`
151	`"0",`
152
153	`# commenting this out because the definite integral of this one`
154	`# between 0 and pi was incorrect AND the indefinite integral`
155	`# became incorrect after I avoided having roots in the denominator`
156	`# when doing multiplications. The two things combined made me`
157	`# think to eliminate this test.`
158	`#77`
159	`#"integral(1/(2+3X^4),X)-1/21/2(2/3/4)^(1/4)(1/2log((X^2+2(2/3/4)^(1/4)X+2(2/3/4)^(1/2))/(X^2-2(2/3/4)^(1/4)X+2(2/3/4)^(1/2)))+arctan(2(2/3/4)^(1/4)X/(2(2/3/4)^(1/2)-X^2)))",`
160	`#"0",`
161
162	`# commenting this out because the definite integral of this one`
163	`# between 0 and pi was incorrect AND the indefinite integral`
164	`# became incorrect after I avoided having roots in the denominator`
165	`# when doing multiplications. The two things combined made me`
166	`# think to eliminate this test.`
167	`#78`
168	`#"integral(1/(2-3X^4),X)-1/2(2/3)^(1/4)/2(1/2log((X+(2/3)^(1/4))/(X-(2/3)^(1/4)))+arctan(X*(2/3)^(-1/4)))",`
169	`#"0",`
170
171	`#79`
172	`"integral(X/(2+3X^4),X)-1/21/31/sqrt(2/3)arctan(X^2/sqrt(2/3))",`
173	`"0",`
174
175	`#80`
176	`"integral(X/(2-3X^4),X)+1/41/3sqrt(3/2)log((X^2-sqrt(2/3))/(X^2+sqrt(2/3)))",`
177	`"0",`
178
179	`# commenting this out because the definite integral of this one`
180	`# between 0 and pi was incorrect AND the indefinite integral`
181	`# became incorrect after I avoided having roots in the denominator`
182	`# when doing multiplications. The two things combined made me`
183	`# think to eliminate this test.`
184	`#81`
185	`#"integral(X^2/(2+3X^4),X)-1/41/3(2/3/4)^(-1/4)(1/2log((X^2-2(2/3/4)^(1/4)X+2sqrt(2/3/4))/(X^2+2(2/3/4)^(1/4)X+2sqrt(2/3/4)))+arctan(2(2/3/4)^(1/4)X/(2sqrt(2/3/4)-X^2)))",`
186	`#"0",`
187
188	`# commenting this out because the definite integral of this one`
189	`# between 0 and pi was incorrect AND the indefinite integral`
190	`# became incorrect after I avoided having roots in the denominator`
191	`# when doing multiplications. The two things combined made me`
192	`# think to eliminate this test.`
193	`#82`
194	`#"integral(X^2/(2-3X^4),X)+1/41/3(2/3)^(-1/4)(log((X-(2/3)^(1/4))/(X+(2/3)^(1/4)))+2arctan(X(2/3)^(-1/4)))",`
195	`#"0",`
196
197	`#83`
198	`"integral(X^3/(A+BX^4),X)-1/41/Blog(A+BX^4)",`
199	`"0",`
200
201	`#124`
202	`"integral(sqrt(A+BX),X)-2/3/Bsqrt((A+B*X)^3)",`
203	`"0",`
204
205	`#125`
206	`"integral(Xsqrt(A+BX),X)+2(2A-3BX)sqrt((A+BX)^3)/15*B^(-2)",`
207	`"0",`
208
209	`#126`
210	`"integral(X^2sqrt(A+BX),X)-2(8A^2-12ABX+15B^2X^2)sqrt((A+BX)^3)/105B^(-3)",`
211	`"0",`
212
213	`#128`
214	`"integral(sqrt(A+BX)/X,X)-2sqrt(A+BX)-Aintegral(1/X1/sqrt(A+BX),X)",`
215	`"0",`
216
217	`#129`
218	`"integral(sqrt(A+BX)/X^2,X)+sqrt(A+BX)/X-B/2integral(1/X1/sqrt(A+B*X),X)",`
219	`"0",`
220
221	`#131`
222	`"integral(1/sqrt(A+BX),X)-2sqrt(A+B*X)/B",`
223	`"0",`
224
225	`#132`
226	`"integral(X/sqrt(A+BX),X)+2/3(2A-BX)sqrt(A+BX)/B^2",`
227	`"0",`
228
229	`#133`
230	`"integral(X^2/sqrt(A+BX),X)-2/15(8A^2-4ABX+3B^2X^2)sqrt(A+BX)/B^3",`
231	`"0",`
232
233	`#134`
234	`"integral(1/X1/sqrt(2+BX),X)-1/sqrt(2)log((sqrt(2+BX)-sqrt(2))/(sqrt(2+B*X)+sqrt(2)))",`
235	`"0",`
236
237	`#136`
238	`"integral(1/X1/sqrt(-2+BX),X)-2/sqrt(2)arctan(sqrt((-2+BX)/2))",`
239	`"0",`
240
241	`#137`
242	`"integral(1/X^21/sqrt(A+BX),X)+sqrt(A+BX)/A/X+1/2B/Aintegral(1/X1/sqrt(A+B*X),X)",`
243	`"0",`
244
245	`#156`
246	`"integral(sqrt(X^2+A),X)-1/2(Xsqrt(X^2+A)+A*log(X+sqrt(X^2+A)))",`
247	`"0",`
248
249	`#157`
250	`"integral(1/sqrt(X^2+A),X)-log(X+sqrt(X^2+A))",`
251	`"0",`
252
253	`#158`
254	`"integral(1/X*1/sqrt(X^2-2),X)-arcsec(X/sqrt(2))/sqrt(2)",`
255	`"0",`
256
257	`#159`
258	`"integral(1/X1/sqrt(X^2+2),X)+1/sqrt(2)log((sqrt(2)+sqrt(X^2+2))/X)",`
259	`"0",`
260
261	`#160`
262	`"integral(sqrt(X^2+2)/X,X)-sqrt(X^2+2)+sqrt(2)*log((sqrt(2)+sqrt(X^2+2))/X)",`
263	`"0",`
264
265	`#161`
266	`"integral(sqrt(X^2-2)/X,X)-sqrt(X^2-2)+sqrt(2)*arcsec(X/sqrt(2))",`
267	`"0",`
268
269	`#162`
270	`"integral(X/sqrt(X^2+A),X)-sqrt(X^2+A)",`
271	`"0",`
272
273	`#163`
274	`"integral(Xsqrt(X^2+A),X)-1/3sqrt((X^2+A)^3)",`
275	`"0",`
276
277	`#164 fails after Jan 2017 changes to abs/mag`
278	`#"integral(sqrt((X^2+A)^3),X)-1/4(Xsqrt((X^2+A)^3)+3/2AXsqrt(X^2+A)+3/2A^2*log(X+sqrt(X^2+A)))",`
279	`#"0",`
280
281	`#"integral(sqrt((X^2-A)^3),X)-1/4(Xsqrt((X^2-A)^3)-3/2AXsqrt(X^2-A)+3/2A^2*log(X+sqrt(X^2-A)))",`
282	`#"0",`
283
284	`#165 fails after Jan 2017 changes to abs/mag`
285	`#"integral(1/sqrt((X^2+A)^3),X)-X/A/sqrt(X^2+A)",`
286	`#"0",`
287
288	`#166 fails after Jan 2017 changes to abs/mag`
289	`#"integral(X/sqrt((X^2+A)^3),X)+1/sqrt(X^2+A)",`
290	`#"0",`
291
292	`#167 fails after Jan 2017 changes to abs/mag`
293	`#"integral(Xsqrt((X^2+A)^3),X)-1/5sqrt((X^2+A)^5)",`
294	`#"0",`
295
296	`#168`
297	`"integral(X^2sqrt(X^2+A),X)-1/4Xsqrt((X^2+A)^3)+1/8AXsqrt(X^2+A)+1/8A^2log(X+sqrt(X^2+A))",`
298	`"0",`
299
300	`#169`
301	`"integral(X^3sqrt(X^2+7),X)-(1/5X^2-2/157)sqrt((X^2+7)^3)",`
302	`"0",`
303
304	`#170`
305	`"integral(X^3sqrt(X^2-7),X)-(sqrt((X^2-7)^5)/5+7sqrt((X^2-7)^3)/3)",`
306	`"0",`
307
308	`#171`
309	`"integral(X^2/sqrt(X^2+A),X)-1/2Xsqrt(X^2+A)+1/2Alog(X+sqrt(X^2+A))",`
310	`"0",`
311
312	`#172`
313	`"integral(X^3/sqrt(X^2+A),X)-1/3sqrt((X^2+A)^3)+Asqrt(X^2+A)",`
314	`"0",`
315
316	`#173`
317	`"integral(1/X^2*1/sqrt(X^2+A),X)+sqrt(X^2+A)/A/X",`
318	`"0",`
319
320	`#174`
321	`"integral(1/X^31/sqrt(X^2+2),X)+1/2sqrt(X^2+2)/2/X^2-1/2*log((sqrt(2)+sqrt(X^2+2))/X)/(sqrt(2)^3)",`
322	`"0",`
323
324	`#175`
325	`"integral(1/X^31/sqrt(X^2-2),X)-1/2sqrt(X^2-2)/2/X^2-1/21/(2^(3/2))arcsec(X/(2^(1/2)))",`
326	`"0",`
327
328	`#176+`
329	`"integral(X^2*sqrt((X^2+2^2)^3),X)\`
330	`-1/6Xsqrt((X^2+2^2)^5)\`
331	`+1/24(2^2)X*sqrt((X^2+2^2)^3)\`
332	`+1/16(2^4)Xsqrt(X^2+2^2)\`
333	`+1/16(2^6)log(X+sqrt(X^2+2^2))",`
334	`"0",`
335
336	`#176-`
337	`"integral(X^2*sqrt((X^2-2^2)^3),X)\`
338	`-1/6Xsqrt((X^2-2^2)^5)\`
339	`-1/24(2^2)X*sqrt((X^2-2^2)^3)\`
340	`+1/16(2^4)Xsqrt(X^2-2^2)\`
341	`-1/16(2^6)log(X+sqrt(X^2-2^2))",`
342	`"0",`
343
344	`#177+`
345	`"integral(X^3*sqrt((X^2+7^2)^3),X)\`
346	`-1/7*sqrt((X^2+7^2)^7)\`
347	`+1/5(7^2)sqrt((X^2+7^2)^5)",`
348	`"0",`
349
350	`#177-`
351	`"integral(X^3*sqrt((X^2-7^2)^3),X)\`
352	`-1/7*sqrt((X^2-7^2)^7)\`
353	`-1/5(7^2)sqrt((X^2-7^2)^5)",`
354	`"0",`
355
356	`#196`
357	`"simplify(integral(1/(X-A)/sqrt(X^2-A^2),X)+sqrt(X^2-A^2)/A/(X-A))",`
358	`"0",`
359	`"simplify(1/(X-A)/sqrt(X^2-A^2)-d(integral(1/(X-A)/sqrt(X^2-A^2),X),X))",`
360	`"0",`
361
362	`#197`
363	`"integral(1/(X+A)/sqrt(X^2-A^2),X)-sqrt(X^2-A^2)/A/(X+A)",`
364	`"0",`
365	`"simplify(1/(X+A)/sqrt(X^2-A^2)-d(integral(1/(X+A)/sqrt(X^2-A^2),X),X))",`
366	`"0",`
367
368	`#200`
369	`"integral(sqrt(7-X^2),X)-1/2(Xsqrt(7-X^2)+7*arcsin(X/sqrt(7)))",`
370	`"0",`
371
372	`#201`
373	`"integral(1/sqrt(7-X^2),X)-arcsin(X/sqrt(7))",`
374	`"0",`
375
376	`#202`
377	`"integral(1/X1/sqrt(7-X^2),X)+1/sqrt(7)log((sqrt(7)+sqrt(7-X^2))/X)",`
378	`"0",`
379
380	`#203`
381	`"integral(sqrt(7-X^2)/X,X)\`
382	`-sqrt(7-X^2)+sqrt(7)*log((sqrt(7)+sqrt(7-X^2))/X)",`
383	`"0",`
384
385	`#204`
386	`"integral(X/sqrt(A-X^2),X)\`
387	`+sqrt(A-X^2)",`
388	`"0",`
389
390	`#205`
391	`"integral(X*sqrt(A-X^2),X)\`
392	`+1/3*sqrt((A-X^2)^3)",`
393	`"0",`
394
395	`#210`
396	`"integral(X^2*sqrt(7-X^2),X)\`
397	`+1/4Xsqrt((7-X^2)^3)\`
398	`-7/8(Xsqrt(7-X^2)+7*arcsin(X/sqrt(7)))",`
399	`"0",`
400
401	`#211`
402	`"integral(X^3*sqrt(7-X^2),X)\`
403	`-(-1/5X^2-2/157)*sqrt((7-X^2)^3)",`
404	`"0",`
405
406	`#214`
407	`"integral(X^2/sqrt(7-X^2),X)\`
408	`+X/2*sqrt(7-X^2)\`
409	`-7/2*arcsin(X/sqrt(7))",`
410	`"0",`
411
412	`#215`
413	`"integral(1/X^2*1/sqrt(7-X^2),X)\`
414	`+sqrt(7-X^2)/7/X",`
415	`"0",`
416
417	`#216`
418	`"integral(sqrt(7-X^2)/X^2,X)\`
419	`+sqrt(7-X^2)/X\`
420	`+arcsin(X/sqrt(7))",`
421	`"0",`
422
423	`#217`
424	`"integral(sqrt(7-X^2)/X^3,X)\`
425	`+1/2*sqrt(7-X^2)/X^2\`
426	`-1/2*log((sqrt(7)+sqrt(7-X^2))/X)/sqrt(7)",`
427	`"0",`
428
429	`#218`
430	`"integral(sqrt(7-X^2)/X^4,X)\`
431	`+1/3*sqrt((7-X^2)^3)/7/X^3",`
432	`"0",`
433
434	`#273`
435	`"integral(sqrt(7X^2+C),X)-Xsqrt(7X^2+C)/2-Clog(Xsqrt(7)+sqrt(7X^2+C))/2/sqrt(7)",`
436	`"0",`
437
438	`#274`
439	`"integral(sqrt(-7X^2+C),X)-Xsqrt(-7X^2+C)/2-Carcsin(X*sqrt(7/C))/2/sqrt(7)",`
440	`"0",`
441
442	`#290`
443	`"integral(sin(AX),X)+cos(AX)/A",`
444	`"0",`
445
446	`#291`
447	`"integral(cos(AX),X)-sin(AX)/A",`
448	`"0",`
449
450	`#292`
451	`"integral(tan(AX),X)+log(cos(AX))/A",`
452	`"0",`
453
454	`#293`
455	`"integral(1/tan(AX),X)-log(sin(AX))/A",`
456	`"0",`
457
458	`#294`
459	`"integral(1/cos(AX),X)-log(tan(pi/4+AX/2))/A",`
460	`"0",`
461
462	`#295`
463	`"integral(1/sin(AX),X)-log(tan(AX/2))/A",`
464	`"0",`
465
466	`#296`
467	`"integral(sin(AX)^2,X)-X/2+sin(2AX)/(4A)",`
468	`"0",`
469
470	`#297`
471	`"integral(sin(AX)^3,X)+cos(AX)(sin(AX)^2+2)/(3*A)",`
472	`"0",`
473
474	`#298`
475	`"integral(sin(AX)^4,X)-3/8X+sin(2AX)/(4A)-sin(4AX)/(32A)",`
476	`"0",`
477
478	`#302`
479	`"integral(cos(AX)^2,X)-X/2-sin(2AX)/(4A)",`
480	`"0",`
481
482	`#303`
483	`"integral(cos(AX)^3,X)-sin(AX)(cos(AX)^2+2)/(3*A)",`
484	`"0",`
485
486	`#304`
487	`"integral(cos(AX)^4,X)-3/8X-sin(2AX)/(4A)-sin(4AX)/(32A)",`
488	`"0",`
489
490	`#308`
491	`"integral((1/sin(AX))^2,X)+1/A1/tan(A*X)",`
492	`"0",`
493
494	`#312`
495	`"integral((1/cos(AX))^2,X)-tan(AX)/A",`
496	`"0",`
497
498	`#318`
499	`"integral(sin(AX)cos(AX),X)-sin(AX)^2/(2*A)",`
500	`"0",`
501
502	`#320`
503	`"integral(sin(AX)^2cos(AX)^2,X)+sin(4AX)/(32A)-X/8",`
504	`"0",`
505
506	`#326`
507	`"integral(sin(AX)/cos(AX)/cos(AX),X)-1/(Acos(A*X))",`
508	`"0",`
509
510	`#327`
511	`"integral(sin(AX)^2/cos(AX),X)+sin(AX)/A-log(tan(pi/4+AX/2))/A",`
512	`"0",`
513
514	`#328`
515	`"integral(cos(AX)/sin(AX)^2,X)+1/(Asin(AX))",`
516	`"0",`
517
518	`#329`
519	`"integral(1/sin(AX)/cos(AX),X)-log(tan(A*X))/A",`
520	`"0",`
521
522	`#330`
523	`"integral(1/sin(AX)/cos(AX)^2,X)-(1/cos(AX)+log(tan(AX/2)))/A",`
524	`"0",`
525
526	`#332`
527	`"integral(1/sin(AX)^2/cos(AX),X)-(log(tan(pi/4+AX/2))-1/sin(AX))/A",`
528	`"0",`
529
530	`#333`
531	`"integral(1/sin(AX)^2/cos(AX)^2,X)+2/(Atan(2A*X))",`
532	`"0",`
533
534	`#335`
535	`"integral(sin(A+BX),X)+cos(A+BX)/B",`
536	`"0",`
537
538	`#336`
539	`"integral(cos(A+BX),X)-sin(A+BX)/B",`
540	`"0",`
541
542	`#337+`
543	`"integral(1/(1+sin(AX)),X)+tan(pi/4-AX/2)/A",`
544	`"0",`
545
546	`#337b+`
547	`"integral(1/(B+Bsin(AX)),X)+tan(pi/4-A*X/2)/A/B",`
548	`"0",`
549
550	`#337-`
551	`"integral(1/(1-sin(AX)),X)-tan(pi/4+AX/2)/A",`
552	`"0",`
553
554	`#337b-`
555	`"integral(1/(B-Bsin(AX)),X)-tan(pi/4+A*X/2)/A/B",`
556	`"0",`
557
558	`#338`
559	`"integral(1/(1+cos(AX)),X)-tan(AX/2)/A",`
560	`"0",`
561
562	`#339`
563	`"integral(1/(1-cos(AX)),X)+1/(Atan(A*X/2))",`
564	`"0",`
565
566	`#340`
567	`"integral(1/(A+Bsin(X)),X)-1/sqrt(B^2-A^2)log((Atan(X/2)+B-sqrt(B^2-A^2))/(Atan(X/2)+B+sqrt(B^2-A^2)))",`
568	`"0",`
569
570	`#341`
571	`"integral(1/(A+Bcos(X)),X)-1/sqrt(B^2-A^2)log((sqrt(B^2-A^2)tan(X/2)+A+B)/(sqrt(B^2-A^2)tan(X/2)-A-B))",`
572	`"0",`
573
574	`#389`
575	`"xsin(Ax)-d(integral(xsin(Ax)))",`
576	`"0",`
577
578	`#390`
579	`"x^2sin(Ax)-d(integral(x^2sin(Ax)))",`
580	`"0",`
581
582	`#393`
583	`"xcos(Ax)-d(integral(xcos(Ax)))",`
584	`"0",`
585
586	`#394`
587	`"x^2cos(Ax)-d(integral(x^2cos(Ax)))",`
588	`"0",`
589
590	`#441`
591	`"integral(arcsin(AX),X)-Xarcsin(AX)-sqrt(1-A^2X^2)/A",`
592	`"0",`
593
594	`#442`
595	`"integral(arccos(AX),X)-Xarccos(AX)+sqrt(1-A^2X^2)/A",`
596	`"0",`
597
598	`#443`
599	`"integral(arctan(AX),X)-Xarctan(AX)+log(1+A^2X^2)/(2*A)",`
600	`"0",`
601
602	`#485`
603	`"integral(log(X),X)-X*log(X)+X",`
604	`"0",`
605
606	`#485a`
607	`"integral(log(AX),X)-Xlog(A*X)+X",`
608	`"0",`
609
610	`#486`
611	`"integral(Xlog(X),X)-1/2X^2log(X)+1/4X^2",`
612	`"0",`
613
614	`#486a`
615	`"integral(Xlog(AX),X)-1/2X^2log(AX)+1/4X^2",`
616	`"0",`
617
618	`#487`
619	`"integral(X^2log(AX),X)-1/3X^3log(A*X)+X^3/9",`
620	`"0",`
621
622	`#489`
623	`"integral(log(X)^2,X)-Xlog(X)^2+2Xlog(X)-2X",`
624	`"0",`
625
626	`#493`
627	`"integral(1/X1/log(AX),X)-log(log(A*X))",`
628	`"0",`
629
630	`#499`
631	`"integral(log(AX+B),X)-(AX+B)log(AX+B)/A+X",`
632	`"0",`
633
634	`#500`
635	`"integral(log(AX+B)/X^2,X)-Alog(X)/B+(AX+B)log(A*X+B)/B/X",`
636	`"0",`
637
638	`#554`
639	`"integral(sinh(X),X)-cosh(X)",`
640	`"0",`
641
642	`#555`
643	`"integral(cosh(X),X)-sinh(X)",`
644	`"0",`
645
646	`#556`
647	`"integral(tanh(X),X)-log(cosh(X))",`
648	`"0",`
649
650	`#560`
651	`"integral(Xsinh(X),X)-Xcosh(X)+sinh(X)",`
652	`"0",`
653
654	`#562`
655	`"integral(Xcosh(X),X)-Xsinh(X)+cosh(X)",`
656	`"0",`
657
658	`#566`
659	`"integral(sinh(X)^2,X)-sinh(2*X)/4+X/2",`
660	`"0",`
661
662	`#569`
663	`"integral(tanh(X)^2,X)-X+tanh(X)",`
664	`"0",`
665
666	`#572`
667	`"integral(cosh(X)^2,X)-sinh(2*X)/4-X/2",`
668	`"0",`
669
670	`# test integral(exp(a*x^2))`
671
672	`"integral(exp(ax^2))+isqrt(pi)erf(isqrt(a)*x)/sqrt(a)/2",`
673	`"0",`
674
675	`"integral(exp(-x^2))-sqrt(pi)*erf(x)/2",`
676	`"0",`
677
678	`# before abs/mag changes of Jan 2017`
679	`# this integral gave the more compact result of:`
680	`# sqrt(pi/3)erf(sqrt(3)x)/2`
681	`# but the new given one is still correct`
682	`"integral(exp(-3x^2))-pi^(1/2)erf(3^(1/2)x)/(23^(1/2))",`
683	`"0",`
684
685	`"integral(1/x*1/(a+log(x)),x)-log(a+log(x))",`
686	`"0",`
687
688	`"integral(exp(ax+bx))",`
689	`"exp((a+b)*x)/(a+b)",`
690
691	`"integral(xexp(ax))",`
692	`"-exp(ax)/(a^2)+xexp(a*x)/a",`
693	`"derivative",`
694	`"xexp(ax)",`
695
696	`"integral(xexp(ax+b))",`
697	`"-exp(ax+b)/(a^2)+xexp(a*x+b)/a",`
698	`"derivative",`
699	`"xexp(ax+b)",`
700
701	`"integral(xexp(-ax+b))",`
702	`"-exp(-ax+b)/(a^2)-xexp(-a*x+b)/a",`
703	`"derivative",`
704	`"xexp(-ax+b)",`
705
706	`"integral(x^2exp(ax))",`
707	`"2exp(ax)/(a^3)-2xexp(ax)/(a^2)+x^2exp(a*x)/a",`
708	`"derivative",`
709	`"x^2exp(ax)",`
710
711	`"integral(x^2exp(ax+b))",`
712	`"2exp(ax+b)/(a^3)-2xexp(ax+b)/(a^2)+x^2exp(a*x+b)/a",`
713	`"derivative",`
714	`"x^2exp(ax+b)",`
715
716	`"integral(x^3exp(ax))",`
717	`"-6exp(ax)/(a^4)+6xexp(ax)/(a^3)-3x^2exp(ax)/(a^2)+x^3exp(ax)/a",`
718	`"derivative",`
719	`"x^3exp(ax)",`
720
721	`"integral(x^3exp(ax+b))",`
722	`"-6exp(ax+b)/(a^4)+6xexp(ax+b)/(a^3)-3x^2exp(ax+b)/(a^2)+x^3exp(ax+b)/a",`
723	`"derivative",`
724	`"x^3exp(ax+b)",`
725
726	`# here`
727	`"integral(sqrt(a*x^2+b))",`
728	`"Stop: integral: sorry, could not find a solution",`
729
730	`"integral(x^2(1-x^2)^(3/2))-(xsqrt(1-x^2)(-8x^4+14x^2-3)+3arcsin(x))/48",`
731	`"0",`
732
733	`"integral(x^4(1-x^2)^(3/2))-(-xsqrt(1-x^2)(16x^6-24x^4+2x^2+3)+3*arcsin(x))/128",`
734	`"0",`
735
736	`"integral(x^2(1-x^2)^(5/2))-(xsqrt(1-x^2)(48x^6-136x^4+118x^2-15)+15*arcsin(x))/384",`
737	`"0",`
738	`]`