Datasets:
chenpanli
/
integrals

Dataset card Data Studio Files
xet
 Community
id
stringlengths
9
9
stage
stringclasses
1 value
k
int64
1
1
integrand
stringlengths
2
20
integrand_latex
stringlengths
3
50
integrand_latex_integral
stringlengths
14
61
reference_antiderivative
stringlengths
3
92
category
stringclasses
5 values
variable
stringclasses
1 value
atom-0300
atomic
1
-cos(14*x + 8)
- \cos{\left(14 x + 8 \right)}
\int - \cos{\left(14 x + 8 \right)} \, dx
-sin(14*x + 8)/14
trigonometric
x
atom-0301
atomic
1
-5*cos(15*x + 9)
- 5 \cos{\left(15 x + 9 \right)}
\int - 5 \cos{\left(15 x + 9 \right)} \, dx
-sin(15*x + 9)/3
trigonometric
x
atom-0302
atomic
1
-3*cos(9*x - 7)
- 3 \cos{\left(9 x - 7 \right)}
\int - 3 \cos{\left(9 x - 7 \right)} \, dx
-sin(9*x - 7)/3
trigonometric
x
atom-0303
atomic
1
-5*sin(8*x - 2)
- 5 \sin{\left(8 x - 2 \right)}
\int - 5 \sin{\left(8 x - 2 \right)} \, dx
5*cos(8*x - 2)/8
trigonometric
x
atom-0304
atomic
1
3*tan(7*x - 8)
3 \tan{\left(7 x - 8 \right)}
\int 3 \tan{\left(7 x - 8 \right)} \, dx
3*log(tan(7*x - 8)**2 + 1)/14
trigonometric
x
atom-0305
atomic
1
5*sin(10*x - 4)
5 \sin{\left(10 x - 4 \right)}
\int 5 \sin{\left(10 x - 4 \right)} \, dx
-cos(10*x - 4)/2
trigonometric
x
atom-0306
atomic
1
-5*cos(2*x + 15)
- 5 \cos{\left(2 x + 15 \right)}
\int - 5 \cos{\left(2 x + 15 \right)} \, dx
-5*sin(2*x + 15)/2
trigonometric
x
atom-0307
atomic
1
4*cos(2*x - 3)
4 \cos{\left(2 x - 3 \right)}
\int 4 \cos{\left(2 x - 3 \right)} \, dx
2*sin(2*x - 3)
trigonometric
x
atom-0308
atomic
1
cos(6*x + 12)
\cos{\left(6 x + 12 \right)}
\int \cos{\left(6 x + 12 \right)} \, dx
sin(6*x + 12)/6
trigonometric
x
atom-0309
atomic
1
-3*tan(10*x + 15)
- 3 \tan{\left(10 x + 15 \right)}
\int - 3 \tan{\left(10 x + 15 \right)} \, dx
-3*log(tan(10*x + 15)**2 + 1)/20
trigonometric
x
atom-0310
atomic
1
4*sin(2*x - 12)
4 \sin{\left(2 x - 12 \right)}
\int 4 \sin{\left(2 x - 12 \right)} \, dx
-2*cos(2*x - 12)
trigonometric
x
atom-0311
atomic
1
-4*sin(3*x - 1)
- 4 \sin{\left(3 x - 1 \right)}
\int - 4 \sin{\left(3 x - 1 \right)} \, dx
4*cos(3*x - 1)/3
trigonometric
x
atom-0312
atomic
1
-sin(8*x - 5)
- \sin{\left(8 x - 5 \right)}
\int - \sin{\left(8 x - 5 \right)} \, dx
cos(8*x - 5)/8
trigonometric
x
atom-0313
atomic
1
3*tan(13*x - 1)
3 \tan{\left(13 x - 1 \right)}
\int 3 \tan{\left(13 x - 1 \right)} \, dx
3*log(tan(13*x - 1)**2 + 1)/26
trigonometric
x
atom-0314
atomic
1
3*cos(9*x - 13)
3 \cos{\left(9 x - 13 \right)}
\int 3 \cos{\left(9 x - 13 \right)} \, dx
sin(9*x - 13)/3
trigonometric
x
atom-0315
atomic
1
5*sin(11*x - 11)
5 \sin{\left(11 x - 11 \right)}
\int 5 \sin{\left(11 x - 11 \right)} \, dx
-5*cos(11*x - 11)/11
trigonometric
x
atom-0316
atomic
1
tan(9*x + 10)
\tan{\left(9 x + 10 \right)}
\int \tan{\left(9 x + 10 \right)} \, dx
log(tan(9*x + 10)**2 + 1)/18
trigonometric
x
atom-0317
atomic
1
-5*tan(13*x + 10)
- 5 \tan{\left(13 x + 10 \right)}
\int - 5 \tan{\left(13 x + 10 \right)} \, dx
-5*log(tan(13*x + 10)**2 + 1)/26
trigonometric
x
atom-0318
atomic
1
4*cos(9*x + 3)
4 \cos{\left(9 x + 3 \right)}
\int 4 \cos{\left(9 x + 3 \right)} \, dx
4*sin(9*x + 3)/9
trigonometric
x
atom-0319
atomic
1
4*tan(5*x + 5)
4 \tan{\left(5 x + 5 \right)}
\int 4 \tan{\left(5 x + 5 \right)} \, dx
2*log(tan(5*x + 5)**2 + 1)/5
trigonometric
x
atom-0320
atomic
1
5*cos(5*x + 11)
5 \cos{\left(5 x + 11 \right)}
\int 5 \cos{\left(5 x + 11 \right)} \, dx
sin(5*x + 11)
trigonometric
x
atom-0321
atomic
1
2*cos(5*x - 6)
2 \cos{\left(5 x - 6 \right)}
\int 2 \cos{\left(5 x - 6 \right)} \, dx
2*sin(5*x - 6)/5
trigonometric
x
atom-0322
atomic
1
3*cos(13*x + 6)
3 \cos{\left(13 x + 6 \right)}
\int 3 \cos{\left(13 x + 6 \right)} \, dx
3*sin(13*x + 6)/13
trigonometric
x
atom-0323
atomic
1
-5*cos(4*x - 11)
- 5 \cos{\left(4 x - 11 \right)}
\int - 5 \cos{\left(4 x - 11 \right)} \, dx
-5*sin(4*x - 11)/4
trigonometric
x
atom-0324
atomic
1
-4*tan(4*x + 4)
- 4 \tan{\left(4 x + 4 \right)}
\int - 4 \tan{\left(4 x + 4 \right)} \, dx
-log(tan(4*x + 4)**2 + 1)/2
trigonometric
x
atom-0325
atomic
1
4*tan(2*x + 15)
4 \tan{\left(2 x + 15 \right)}
\int 4 \tan{\left(2 x + 15 \right)} \, dx
log(tan(2*x + 15)**2 + 1)
trigonometric
x
atom-0326
atomic
1
2*tan(14*x + 10)
2 \tan{\left(14 x + 10 \right)}
\int 2 \tan{\left(14 x + 10 \right)} \, dx
log(tan(14*x + 10)**2 + 1)/14
trigonometric
x
atom-0327
atomic
1
4*sin(x - 11)
4 \sin{\left(x - 11 \right)}
\int 4 \sin{\left(x - 11 \right)} \, dx
-4*cos(x - 11)
trigonometric
x
atom-0328
atomic
1
-4*sin(x + 5)
- 4 \sin{\left(x + 5 \right)}
\int - 4 \sin{\left(x + 5 \right)} \, dx
4*cos(x + 5)
trigonometric
x
atom-0329
atomic
1
-2*tan(x - 1)
- 2 \tan{\left(x - 1 \right)}
\int - 2 \tan{\left(x - 1 \right)} \, dx
-log(tan(x - 1)**2 + 1)
trigonometric
x
atom-0330
atomic
1
-cos(3*x + 2)
- \cos{\left(3 x + 2 \right)}
\int - \cos{\left(3 x + 2 \right)} \, dx
-sin(3*x + 2)/3
trigonometric
x
atom-0331
atomic
1
-5*tan(10*x + 5)
- 5 \tan{\left(10 x + 5 \right)}
\int - 5 \tan{\left(10 x + 5 \right)} \, dx
-log(tan(10*x + 5)**2 + 1)/4
trigonometric
x
atom-0332
atomic
1
-4*cos(2*x + 6)
- 4 \cos{\left(2 x + 6 \right)}
\int - 4 \cos{\left(2 x + 6 \right)} \, dx
-2*sin(2*x + 6)
trigonometric
x
atom-0333
atomic
1
5*tan(15*x + 14)
5 \tan{\left(15 x + 14 \right)}
\int 5 \tan{\left(15 x + 14 \right)} \, dx
log(tan(15*x + 14)**2 + 1)/6
trigonometric
x
atom-0334
atomic
1
-4*sin(3*x + 6)
- 4 \sin{\left(3 x + 6 \right)}
\int - 4 \sin{\left(3 x + 6 \right)} \, dx
4*cos(3*x + 6)/3
trigonometric
x
atom-0335
atomic
1
-tan(15*x + 5)
- \tan{\left(15 x + 5 \right)}
\int - \tan{\left(15 x + 5 \right)} \, dx
-log(tan(15*x + 5)**2 + 1)/30
trigonometric
x
atom-0336
atomic
1
-3*sin(4*x + 7)
- 3 \sin{\left(4 x + 7 \right)}
\int - 3 \sin{\left(4 x + 7 \right)} \, dx
3*cos(4*x + 7)/4
trigonometric
x
atom-0337
atomic
1
cos(5*x + 10)
\cos{\left(5 x + 10 \right)}
\int \cos{\left(5 x + 10 \right)} \, dx
sin(5*x + 10)/5
trigonometric
x
atom-0338
atomic
1
5*tan(7*x + 11)
5 \tan{\left(7 x + 11 \right)}
\int 5 \tan{\left(7 x + 11 \right)} \, dx
5*log(tan(7*x + 11)**2 + 1)/14
trigonometric
x
atom-0339
atomic
1
-3*tan(13*x - 5)
- 3 \tan{\left(13 x - 5 \right)}
\int - 3 \tan{\left(13 x - 5 \right)} \, dx
-3*log(tan(13*x - 5)**2 + 1)/26
trigonometric
x
atom-0340
atomic
1
5*sin(4*x + 6)
5 \sin{\left(4 x + 6 \right)}
\int 5 \sin{\left(4 x + 6 \right)} \, dx
-5*cos(4*x + 6)/4
trigonometric
x
atom-0341
atomic
1
-2*sin(9*x + 8)
- 2 \sin{\left(9 x + 8 \right)}
\int - 2 \sin{\left(9 x + 8 \right)} \, dx
2*cos(9*x + 8)/9
trigonometric
x
atom-0342
atomic
1
-sin(12*x + 10)
- \sin{\left(12 x + 10 \right)}
\int - \sin{\left(12 x + 10 \right)} \, dx
cos(12*x + 10)/12
trigonometric
x
atom-0343
atomic
1
3*tan(11*x + 8)
3 \tan{\left(11 x + 8 \right)}
\int 3 \tan{\left(11 x + 8 \right)} \, dx
3*log(tan(11*x + 8)**2 + 1)/22
trigonometric
x
atom-0344
atomic
1
4*cos(11*x - 4)
4 \cos{\left(11 x - 4 \right)}
\int 4 \cos{\left(11 x - 4 \right)} \, dx
4*sin(11*x - 4)/11
trigonometric
x
atom-0345
atomic
1
-3*tan(11*x + 7)
- 3 \tan{\left(11 x + 7 \right)}
\int - 3 \tan{\left(11 x + 7 \right)} \, dx
-3*log(tan(11*x + 7)**2 + 1)/22
trigonometric
x
atom-0346
atomic
1
-3*sin(8*x - 1)
- 3 \sin{\left(8 x - 1 \right)}
\int - 3 \sin{\left(8 x - 1 \right)} \, dx
3*cos(8*x - 1)/8
trigonometric
x
atom-0347
atomic
1
5*cos(8*x - 8)
5 \cos{\left(8 x - 8 \right)}
\int 5 \cos{\left(8 x - 8 \right)} \, dx
5*sin(8*x - 8)/8
trigonometric
x
atom-0348
atomic
1
-2*sin(8*x - 2)
- 2 \sin{\left(8 x - 2 \right)}
\int - 2 \sin{\left(8 x - 2 \right)} \, dx
cos(8*x - 2)/4
trigonometric
x
atom-0349
atomic
1
2*sin(13*x + 11)
2 \sin{\left(13 x + 11 \right)}
\int 2 \sin{\left(13 x + 11 \right)} \, dx
-2*cos(13*x + 11)/13
trigonometric
x
atom-0350
atomic
1
4*cos(x + 1)
4 \cos{\left(x + 1 \right)}
\int 4 \cos{\left(x + 1 \right)} \, dx
4*sin(x + 1)
trigonometric
x
atom-0351
atomic
1
3*sin(x - 2)
3 \sin{\left(x - 2 \right)}
\int 3 \sin{\left(x - 2 \right)} \, dx
-3*cos(x - 2)
trigonometric
x
atom-0352
atomic
1
4*cos(11*x - 12)
4 \cos{\left(11 x - 12 \right)}
\int 4 \cos{\left(11 x - 12 \right)} \, dx
4*sin(11*x - 12)/11
trigonometric
x
atom-0353
atomic
1
2*tan(12*x - 4)
2 \tan{\left(12 x - 4 \right)}
\int 2 \tan{\left(12 x - 4 \right)} \, dx
log(tan(12*x - 4)**2 + 1)/12
trigonometric
x
atom-0354
atomic
1
3*cos(12*x - 12)
3 \cos{\left(12 x - 12 \right)}
\int 3 \cos{\left(12 x - 12 \right)} \, dx
sin(12*x - 12)/4
trigonometric
x
atom-0355
atomic
1
3*tan(7*x + 1)
3 \tan{\left(7 x + 1 \right)}
\int 3 \tan{\left(7 x + 1 \right)} \, dx
3*log(tan(7*x + 1)**2 + 1)/14
trigonometric
x
atom-0356
atomic
1
-sin(13*x - 15)
- \sin{\left(13 x - 15 \right)}
\int - \sin{\left(13 x - 15 \right)} \, dx
cos(13*x - 15)/13
trigonometric
x
atom-0357
atomic
1
-5*cos(2*x + 14)
- 5 \cos{\left(2 x + 14 \right)}
\int - 5 \cos{\left(2 x + 14 \right)} \, dx
-5*sin(2*x + 14)/2
trigonometric
x
atom-0358
atomic
1
-2*cos(3*x + 13)
- 2 \cos{\left(3 x + 13 \right)}
\int - 2 \cos{\left(3 x + 13 \right)} \, dx
-2*sin(3*x + 13)/3
trigonometric
x
atom-0359
atomic
1
-4*tan(11*x + 7)
- 4 \tan{\left(11 x + 7 \right)}
\int - 4 \tan{\left(11 x + 7 \right)} \, dx
-2*log(tan(11*x + 7)**2 + 1)/11
trigonometric
x
atom-0360
atomic
1
-3*cos(11*x + 14)
- 3 \cos{\left(11 x + 14 \right)}
\int - 3 \cos{\left(11 x + 14 \right)} \, dx
-3*sin(11*x + 14)/11
trigonometric
x
atom-0361
atomic
1
2*sin(7*x + 11)
2 \sin{\left(7 x + 11 \right)}
\int 2 \sin{\left(7 x + 11 \right)} \, dx
-2*cos(7*x + 11)/7
trigonometric
x
atom-0362
atomic
1
-2*sin(x - 4)
- 2 \sin{\left(x - 4 \right)}
\int - 2 \sin{\left(x - 4 \right)} \, dx
2*cos(x - 4)
trigonometric
x
atom-0363
atomic
1
5*sin(7*x + 9)
5 \sin{\left(7 x + 9 \right)}
\int 5 \sin{\left(7 x + 9 \right)} \, dx
-5*cos(7*x + 9)/7
trigonometric
x
atom-0364
atomic
1
4*sin(x - 2)
4 \sin{\left(x - 2 \right)}
\int 4 \sin{\left(x - 2 \right)} \, dx
-4*cos(x - 2)
trigonometric
x
atom-0365
atomic
1
2*sin(6*x + 12)
2 \sin{\left(6 x + 12 \right)}
\int 2 \sin{\left(6 x + 12 \right)} \, dx
-cos(6*x + 12)/3
trigonometric
x
atom-0366
atomic
1
5*cos(10*x + 4)
5 \cos{\left(10 x + 4 \right)}
\int 5 \cos{\left(10 x + 4 \right)} \, dx
sin(10*x + 4)/2
trigonometric
x
atom-0367
atomic
1
2*sin(4*x + 2)
2 \sin{\left(4 x + 2 \right)}
\int 2 \sin{\left(4 x + 2 \right)} \, dx
-cos(4*x + 2)/2
trigonometric
x
atom-0368
atomic
1
-4*sin(8*x - 7)
- 4 \sin{\left(8 x - 7 \right)}
\int - 4 \sin{\left(8 x - 7 \right)} \, dx
cos(8*x - 7)/2
trigonometric
x
atom-0369
atomic
1
-5*sin(4*x - 4)
- 5 \sin{\left(4 x - 4 \right)}
\int - 5 \sin{\left(4 x - 4 \right)} \, dx
5*cos(4*x - 4)/4
trigonometric
x
atom-0370
atomic
1
-3*sin(6*x + 6)
- 3 \sin{\left(6 x + 6 \right)}
\int - 3 \sin{\left(6 x + 6 \right)} \, dx
cos(6*x + 6)/2
trigonometric
x
atom-0371
atomic
1
-4*tan(15*x + 1)
- 4 \tan{\left(15 x + 1 \right)}
\int - 4 \tan{\left(15 x + 1 \right)} \, dx
-2*log(tan(15*x + 1)**2 + 1)/15
trigonometric
x
atom-0372
atomic
1
3*cos(2*x - 15)
3 \cos{\left(2 x - 15 \right)}
\int 3 \cos{\left(2 x - 15 \right)} \, dx
3*sin(2*x - 15)/2
trigonometric
x
atom-0373
atomic
1
-5*cos(5*x - 3)
- 5 \cos{\left(5 x - 3 \right)}
\int - 5 \cos{\left(5 x - 3 \right)} \, dx
-sin(5*x - 3)
trigonometric
x
atom-0374
atomic
1
5*sin(4*x - 10)
5 \sin{\left(4 x - 10 \right)}
\int 5 \sin{\left(4 x - 10 \right)} \, dx
-5*cos(4*x - 10)/4
trigonometric
x
atom-0375
atomic
1
5*tan(5*x - 12)
5 \tan{\left(5 x - 12 \right)}
\int 5 \tan{\left(5 x - 12 \right)} \, dx
log(tan(5*x - 12)**2 + 1)/2
trigonometric
x
atom-0376
atomic
1
3*tan(14*x + 4)
3 \tan{\left(14 x + 4 \right)}
\int 3 \tan{\left(14 x + 4 \right)} \, dx
3*log(tan(14*x + 4)**2 + 1)/28
trigonometric
x
atom-0377
atomic
1
-5*tan(10*x - 11)
- 5 \tan{\left(10 x - 11 \right)}
\int - 5 \tan{\left(10 x - 11 \right)} \, dx
-log(tan(10*x - 11)**2 + 1)/4
trigonometric
x
atom-0378
atomic
1
2*sin(5*x - 10)
2 \sin{\left(5 x - 10 \right)}
\int 2 \sin{\left(5 x - 10 \right)} \, dx
-2*cos(5*x - 10)/5
trigonometric
x
atom-0379
atomic
1
-2*sin(14*x + 6)
- 2 \sin{\left(14 x + 6 \right)}
\int - 2 \sin{\left(14 x + 6 \right)} \, dx
cos(14*x + 6)/7
trigonometric
x
atom-0380
atomic
1
-2*cos(13*x - 14)
- 2 \cos{\left(13 x - 14 \right)}
\int - 2 \cos{\left(13 x - 14 \right)} \, dx
-2*sin(13*x - 14)/13
trigonometric
x
atom-0381
atomic
1
-3*tan(3*x - 11)
- 3 \tan{\left(3 x - 11 \right)}
\int - 3 \tan{\left(3 x - 11 \right)} \, dx
-log(tan(3*x - 11)**2 + 1)/2
trigonometric
x
atom-0382
atomic
1
-5*sin(9*x + 5)
- 5 \sin{\left(9 x + 5 \right)}
\int - 5 \sin{\left(9 x + 5 \right)} \, dx
5*cos(9*x + 5)/9
trigonometric
x
atom-0383
atomic
1
-5*cos(12*x + 5)
- 5 \cos{\left(12 x + 5 \right)}
\int - 5 \cos{\left(12 x + 5 \right)} \, dx
-5*sin(12*x + 5)/12
trigonometric
x
atom-0384
atomic
1
tan(13*x - 3)
\tan{\left(13 x - 3 \right)}
\int \tan{\left(13 x - 3 \right)} \, dx
log(tan(13*x - 3)**2 + 1)/26
trigonometric
x
atom-0385
atomic
1
4*sin(2*x - 4)
4 \sin{\left(2 x - 4 \right)}
\int 4 \sin{\left(2 x - 4 \right)} \, dx
-2*cos(2*x - 4)
trigonometric
x
atom-0386
atomic
1
4*tan(13*x + 5)
4 \tan{\left(13 x + 5 \right)}
\int 4 \tan{\left(13 x + 5 \right)} \, dx
2*log(tan(13*x + 5)**2 + 1)/13
trigonometric
x
atom-0387
atomic
1
2*cos(4*x + 7)
2 \cos{\left(4 x + 7 \right)}
\int 2 \cos{\left(4 x + 7 \right)} \, dx
sin(4*x + 7)/2
trigonometric
x
atom-0388
atomic
1
-2*sin(4*x + 1)
- 2 \sin{\left(4 x + 1 \right)}
\int - 2 \sin{\left(4 x + 1 \right)} \, dx
cos(4*x + 1)/2
trigonometric
x
atom-0389
atomic
1
-4*tan(2*x + 7)
- 4 \tan{\left(2 x + 7 \right)}
\int - 4 \tan{\left(2 x + 7 \right)} \, dx
-log(tan(2*x + 7)**2 + 1)
trigonometric
x
atom-0390
atomic
1
5*tan(13*x - 6)
5 \tan{\left(13 x - 6 \right)}
\int 5 \tan{\left(13 x - 6 \right)} \, dx
5*log(tan(13*x - 6)**2 + 1)/26
trigonometric
x
atom-0391
atomic
1
3*tan(10*x + 8)
3 \tan{\left(10 x + 8 \right)}
\int 3 \tan{\left(10 x + 8 \right)} \, dx
3*log(tan(10*x + 8)**2 + 1)/20
trigonometric
x
atom-0392
atomic
1
5*tan(11*x - 12)
5 \tan{\left(11 x - 12 \right)}
\int 5 \tan{\left(11 x - 12 \right)} \, dx
5*log(tan(11*x - 12)**2 + 1)/22
trigonometric
x
atom-0393
atomic
1
-2*sin(14*x + 11)
- 2 \sin{\left(14 x + 11 \right)}
\int - 2 \sin{\left(14 x + 11 \right)} \, dx
cos(14*x + 11)/7
trigonometric
x
atom-0394
atomic
1
5*cos(4*x + 4)
5 \cos{\left(4 x + 4 \right)}
\int 5 \cos{\left(4 x + 4 \right)} \, dx
5*sin(4*x + 4)/4
trigonometric
x
atom-0395
atomic
1
-5*tan(4*x - 11)
- 5 \tan{\left(4 x - 11 \right)}
\int - 5 \tan{\left(4 x - 11 \right)} \, dx
-5*log(tan(4*x - 11)**2 + 1)/8
trigonometric
x
atom-0396
atomic
1
2*tan(9*x - 13)
2 \tan{\left(9 x - 13 \right)}
\int 2 \tan{\left(9 x - 13 \right)} \, dx
log(tan(9*x - 13)**2 + 1)/9
trigonometric
x
atom-0397
atomic
1
cos(5*x - 5)
\cos{\left(5 x - 5 \right)}
\int \cos{\left(5 x - 5 \right)} \, dx
sin(5*x - 5)/5
trigonometric
x
atom-0398
atomic
1
4*sin(15*x - 8)
4 \sin{\left(15 x - 8 \right)}
\int 4 \sin{\left(15 x - 8 \right)} \, dx
-4*cos(15*x - 8)/15
trigonometric
x
atom-0399
atomic
1
sin(14*x + 2)
\sin{\left(14 x + 2 \right)}
\int \sin{\left(14 x + 2 \right)} \, dx
-cos(14*x + 2)/14
trigonometric
x