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