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-0200
atomic
1
2*cos(7*x + 14)
2 \cos{\left(7 x + 14 \right)}
\int 2 \cos{\left(7 x + 14 \right)} \, dx
2*sin(7*x + 14)/7
trigonometric
x
atom-0201
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-0202
atomic
1
2*sin(15*x - 14)
2 \sin{\left(15 x - 14 \right)}
\int 2 \sin{\left(15 x - 14 \right)} \, dx
-2*cos(15*x - 14)/15
trigonometric
x
atom-0203
atomic
1
-4*sin(5*x - 12)
- 4 \sin{\left(5 x - 12 \right)}
\int - 4 \sin{\left(5 x - 12 \right)} \, dx
4*cos(5*x - 12)/5
trigonometric
x
atom-0204
atomic
1
2*cos(12*x - 1)
2 \cos{\left(12 x - 1 \right)}
\int 2 \cos{\left(12 x - 1 \right)} \, dx
sin(12*x - 1)/6
trigonometric
x
atom-0205
atomic
1
3*tan(2*x - 12)
3 \tan{\left(2 x - 12 \right)}
\int 3 \tan{\left(2 x - 12 \right)} \, dx
3*log(tan(2*x - 12)**2 + 1)/4
trigonometric
x
atom-0206
atomic
1
-4*cos(10*x - 7)
- 4 \cos{\left(10 x - 7 \right)}
\int - 4 \cos{\left(10 x - 7 \right)} \, dx
-2*sin(10*x - 7)/5
trigonometric
x
atom-0207
atomic
1
cos(5*x - 13)
\cos{\left(5 x - 13 \right)}
\int \cos{\left(5 x - 13 \right)} \, dx
sin(5*x - 13)/5
trigonometric
x
atom-0208
atomic
1
3*cos(3*x - 15)
3 \cos{\left(3 x - 15 \right)}
\int 3 \cos{\left(3 x - 15 \right)} \, dx
sin(3*x - 15)
trigonometric
x
atom-0209
atomic
1
2*sin(12*x + 2)
2 \sin{\left(12 x + 2 \right)}
\int 2 \sin{\left(12 x + 2 \right)} \, dx
-cos(12*x + 2)/6
trigonometric
x
atom-0210
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-0211
atomic
1
4*tan(2*x + 12)
4 \tan{\left(2 x + 12 \right)}
\int 4 \tan{\left(2 x + 12 \right)} \, dx
log(tan(2*x + 12)**2 + 1)
trigonometric
x
atom-0212
atomic
1
4*tan(x + 10)
4 \tan{\left(x + 10 \right)}
\int 4 \tan{\left(x + 10 \right)} \, dx
2*log(tan(x + 10)**2 + 1)
trigonometric
x
atom-0213
atomic
1
5*sin(14*x + 5)
5 \sin{\left(14 x + 5 \right)}
\int 5 \sin{\left(14 x + 5 \right)} \, dx
-5*cos(14*x + 5)/14
trigonometric
x
atom-0214
atomic
1
-tan(11*x + 8)
- \tan{\left(11 x + 8 \right)}
\int - \tan{\left(11 x + 8 \right)} \, dx
-log(tan(11*x + 8)**2 + 1)/22
trigonometric
x
atom-0215
atomic
1
5*sin(10*x - 10)
5 \sin{\left(10 x - 10 \right)}
\int 5 \sin{\left(10 x - 10 \right)} \, dx
-cos(10*x - 10)/2
trigonometric
x
atom-0216
atomic
1
4*tan(12*x - 3)
4 \tan{\left(12 x - 3 \right)}
\int 4 \tan{\left(12 x - 3 \right)} \, dx
log(tan(12*x - 3)**2 + 1)/6
trigonometric
x
atom-0217
atomic
1
2*sin(14*x + 3)
2 \sin{\left(14 x + 3 \right)}
\int 2 \sin{\left(14 x + 3 \right)} \, dx
-cos(14*x + 3)/7
trigonometric
x
atom-0218
atomic
1
5*cos(7*x + 1)
5 \cos{\left(7 x + 1 \right)}
\int 5 \cos{\left(7 x + 1 \right)} \, dx
5*sin(7*x + 1)/7
trigonometric
x
atom-0219
atomic
1
2*tan(13*x - 6)
2 \tan{\left(13 x - 6 \right)}
\int 2 \tan{\left(13 x - 6 \right)} \, dx
log(tan(13*x - 6)**2 + 1)/13
trigonometric
x
atom-0220
atomic
1
-4*cos(x - 15)
- 4 \cos{\left(x - 15 \right)}
\int - 4 \cos{\left(x - 15 \right)} \, dx
-4*sin(x - 15)
trigonometric
x
atom-0221
atomic
1
-cos(5*x + 15)
- \cos{\left(5 x + 15 \right)}
\int - \cos{\left(5 x + 15 \right)} \, dx
-sin(5*x + 15)/5
trigonometric
x
atom-0222
atomic
1
2*sin(12*x - 6)
2 \sin{\left(12 x - 6 \right)}
\int 2 \sin{\left(12 x - 6 \right)} \, dx
-cos(12*x - 6)/6
trigonometric
x
atom-0223
atomic
1
2*cos(12*x + 8)
2 \cos{\left(12 x + 8 \right)}
\int 2 \cos{\left(12 x + 8 \right)} \, dx
sin(12*x + 8)/6
trigonometric
x
atom-0224
atomic
1
4*cos(6*x - 7)
4 \cos{\left(6 x - 7 \right)}
\int 4 \cos{\left(6 x - 7 \right)} \, dx
2*sin(6*x - 7)/3
trigonometric
x
atom-0225
atomic
1
-5*sin(3*x + 7)
- 5 \sin{\left(3 x + 7 \right)}
\int - 5 \sin{\left(3 x + 7 \right)} \, dx
5*cos(3*x + 7)/3
trigonometric
x
atom-0226
atomic
1
5*sin(9*x + 8)
5 \sin{\left(9 x + 8 \right)}
\int 5 \sin{\left(9 x + 8 \right)} \, dx
-5*cos(9*x + 8)/9
trigonometric
x
atom-0227
atomic
1
2*cos(11*x + 13)
2 \cos{\left(11 x + 13 \right)}
\int 2 \cos{\left(11 x + 13 \right)} \, dx
2*sin(11*x + 13)/11
trigonometric
x
atom-0228
atomic
1
-2*cos(4*x + 10)
- 2 \cos{\left(4 x + 10 \right)}
\int - 2 \cos{\left(4 x + 10 \right)} \, dx
-sin(4*x + 10)/2
trigonometric
x
atom-0229
atomic
1
-2*tan(4*x - 7)
- 2 \tan{\left(4 x - 7 \right)}
\int - 2 \tan{\left(4 x - 7 \right)} \, dx
-log(tan(4*x - 7)**2 + 1)/4
trigonometric
x
atom-0230
atomic
1
5*sin(6*x + 11)
5 \sin{\left(6 x + 11 \right)}
\int 5 \sin{\left(6 x + 11 \right)} \, dx
-5*cos(6*x + 11)/6
trigonometric
x
atom-0231
atomic
1
5*cos(5*x - 14)
5 \cos{\left(5 x - 14 \right)}
\int 5 \cos{\left(5 x - 14 \right)} \, dx
sin(5*x - 14)
trigonometric
x
atom-0232
atomic
1
-5*tan(3*x - 4)
- 5 \tan{\left(3 x - 4 \right)}
\int - 5 \tan{\left(3 x - 4 \right)} \, dx
-5*log(tan(3*x - 4)**2 + 1)/6
trigonometric
x
atom-0233
atomic
1
-cos(5*x - 8)
- \cos{\left(5 x - 8 \right)}
\int - \cos{\left(5 x - 8 \right)} \, dx
-sin(5*x - 8)/5
trigonometric
x
atom-0234
atomic
1
-3*cos(10*x + 2)
- 3 \cos{\left(10 x + 2 \right)}
\int - 3 \cos{\left(10 x + 2 \right)} \, dx
-3*sin(10*x + 2)/10
trigonometric
x
atom-0235
atomic
1
-cos(11*x - 10)
- \cos{\left(11 x - 10 \right)}
\int - \cos{\left(11 x - 10 \right)} \, dx
-sin(11*x - 10)/11
trigonometric
x
atom-0236
atomic
1
2*cos(15*x + 10)
2 \cos{\left(15 x + 10 \right)}
\int 2 \cos{\left(15 x + 10 \right)} \, dx
2*sin(15*x + 10)/15
trigonometric
x
atom-0237
atomic
1
4*sin(x - 15)
4 \sin{\left(x - 15 \right)}
\int 4 \sin{\left(x - 15 \right)} \, dx
-4*cos(x - 15)
trigonometric
x
atom-0238
atomic
1
-2*tan(12*x + 6)
- 2 \tan{\left(12 x + 6 \right)}
\int - 2 \tan{\left(12 x + 6 \right)} \, dx
-log(tan(12*x + 6)**2 + 1)/12
trigonometric
x
atom-0239
atomic
1
tan(15*x + 12)
\tan{\left(15 x + 12 \right)}
\int \tan{\left(15 x + 12 \right)} \, dx
log(tan(15*x + 12)**2 + 1)/30
trigonometric
x
atom-0240
atomic
1
-tan(15*x + 7)
- \tan{\left(15 x + 7 \right)}
\int - \tan{\left(15 x + 7 \right)} \, dx
-log(tan(15*x + 7)**2 + 1)/30
trigonometric
x
atom-0241
atomic
1
5*cos(8*x + 6)
5 \cos{\left(8 x + 6 \right)}
\int 5 \cos{\left(8 x + 6 \right)} \, dx
5*sin(8*x + 6)/8
trigonometric
x
atom-0242
atomic
1
5*sin(15*x - 4)
5 \sin{\left(15 x - 4 \right)}
\int 5 \sin{\left(15 x - 4 \right)} \, dx
-cos(15*x - 4)/3
trigonometric
x
atom-0243
atomic
1
-2*tan(15*x - 4)
- 2 \tan{\left(15 x - 4 \right)}
\int - 2 \tan{\left(15 x - 4 \right)} \, dx
-log(tan(15*x - 4)**2 + 1)/15
trigonometric
x
atom-0244
atomic
1
-4*sin(8*x - 5)
- 4 \sin{\left(8 x - 5 \right)}
\int - 4 \sin{\left(8 x - 5 \right)} \, dx
cos(8*x - 5)/2
trigonometric
x
atom-0245
atomic
1
2*cos(14*x + 7)
2 \cos{\left(14 x + 7 \right)}
\int 2 \cos{\left(14 x + 7 \right)} \, dx
sin(14*x + 7)/7
trigonometric
x
atom-0246
atomic
1
4*sin(11*x + 14)
4 \sin{\left(11 x + 14 \right)}
\int 4 \sin{\left(11 x + 14 \right)} \, dx
-4*cos(11*x + 14)/11
trigonometric
x
atom-0247
atomic
1
-2*sin(12*x + 12)
- 2 \sin{\left(12 x + 12 \right)}
\int - 2 \sin{\left(12 x + 12 \right)} \, dx
cos(12*x + 12)/6
trigonometric
x
atom-0248
atomic
1
-3*cos(3*x + 1)
- 3 \cos{\left(3 x + 1 \right)}
\int - 3 \cos{\left(3 x + 1 \right)} \, dx
-sin(3*x + 1)
trigonometric
x
atom-0249
atomic
1
-3*tan(2*x - 3)
- 3 \tan{\left(2 x - 3 \right)}
\int - 3 \tan{\left(2 x - 3 \right)} \, dx
-3*log(tan(2*x - 3)**2 + 1)/4
trigonometric
x
atom-0250
atomic
1
cos(5*x - 12)
\cos{\left(5 x - 12 \right)}
\int \cos{\left(5 x - 12 \right)} \, dx
sin(5*x - 12)/5
trigonometric
x
atom-0251
atomic
1
-cos(14*x - 7)
- \cos{\left(14 x - 7 \right)}
\int - \cos{\left(14 x - 7 \right)} \, dx
-sin(14*x - 7)/14
trigonometric
x
atom-0252
atomic
1
2*cos(15*x - 8)
2 \cos{\left(15 x - 8 \right)}
\int 2 \cos{\left(15 x - 8 \right)} \, dx
2*sin(15*x - 8)/15
trigonometric
x
atom-0253
atomic
1
-5*tan(4*x - 2)
- 5 \tan{\left(4 x - 2 \right)}
\int - 5 \tan{\left(4 x - 2 \right)} \, dx
-5*log(tan(4*x - 2)**2 + 1)/8
trigonometric
x
atom-0254
atomic
1
-sin(7*x + 9)
- \sin{\left(7 x + 9 \right)}
\int - \sin{\left(7 x + 9 \right)} \, dx
cos(7*x + 9)/7
trigonometric
x
atom-0255
atomic
1
-2*sin(13*x - 6)
- 2 \sin{\left(13 x - 6 \right)}
\int - 2 \sin{\left(13 x - 6 \right)} \, dx
2*cos(13*x - 6)/13
trigonometric
x
atom-0256
atomic
1
4*cos(15*x + 14)
4 \cos{\left(15 x + 14 \right)}
\int 4 \cos{\left(15 x + 14 \right)} \, dx
4*sin(15*x + 14)/15
trigonometric
x
atom-0257
atomic
1
-3*sin(10*x + 3)
- 3 \sin{\left(10 x + 3 \right)}
\int - 3 \sin{\left(10 x + 3 \right)} \, dx
3*cos(10*x + 3)/10
trigonometric
x
atom-0258
atomic
1
-3*sin(9*x - 3)
- 3 \sin{\left(9 x - 3 \right)}
\int - 3 \sin{\left(9 x - 3 \right)} \, dx
cos(9*x - 3)/3
trigonometric
x
atom-0259
atomic
1
2*sin(5*x - 9)
2 \sin{\left(5 x - 9 \right)}
\int 2 \sin{\left(5 x - 9 \right)} \, dx
-2*cos(5*x - 9)/5
trigonometric
x
atom-0260
atomic
1
-4*sin(15*x + 7)
- 4 \sin{\left(15 x + 7 \right)}
\int - 4 \sin{\left(15 x + 7 \right)} \, dx
4*cos(15*x + 7)/15
trigonometric
x
atom-0261
atomic
1
-3*sin(7*x - 10)
- 3 \sin{\left(7 x - 10 \right)}
\int - 3 \sin{\left(7 x - 10 \right)} \, dx
3*cos(7*x - 10)/7
trigonometric
x
atom-0262
atomic
1
-5*cos(11*x + 15)
- 5 \cos{\left(11 x + 15 \right)}
\int - 5 \cos{\left(11 x + 15 \right)} \, dx
-5*sin(11*x + 15)/11
trigonometric
x
atom-0263
atomic
1
-2*sin(3*x - 5)
- 2 \sin{\left(3 x - 5 \right)}
\int - 2 \sin{\left(3 x - 5 \right)} \, dx
2*cos(3*x - 5)/3
trigonometric
x
atom-0264
atomic
1
-5*cos(11*x - 8)
- 5 \cos{\left(11 x - 8 \right)}
\int - 5 \cos{\left(11 x - 8 \right)} \, dx
-5*sin(11*x - 8)/11
trigonometric
x
atom-0265
atomic
1
-4*cos(x - 9)
- 4 \cos{\left(x - 9 \right)}
\int - 4 \cos{\left(x - 9 \right)} \, dx
-4*sin(x - 9)
trigonometric
x
atom-0266
atomic
1
4*sin(x - 1)
4 \sin{\left(x - 1 \right)}
\int 4 \sin{\left(x - 1 \right)} \, dx
-4*cos(x - 1)
trigonometric
x
atom-0267
atomic
1
-5*tan(8*x + 10)
- 5 \tan{\left(8 x + 10 \right)}
\int - 5 \tan{\left(8 x + 10 \right)} \, dx
-5*log(tan(8*x + 10)**2 + 1)/16
trigonometric
x
atom-0268
atomic
1
2*sin(5*x + 15)
2 \sin{\left(5 x + 15 \right)}
\int 2 \sin{\left(5 x + 15 \right)} \, dx
-2*cos(5*x + 15)/5
trigonometric
x
atom-0269
atomic
1
2*cos(12*x - 3)
2 \cos{\left(12 x - 3 \right)}
\int 2 \cos{\left(12 x - 3 \right)} \, dx
sin(12*x - 3)/6
trigonometric
x
atom-0270
atomic
1
4*sin(5*x - 4)
4 \sin{\left(5 x - 4 \right)}
\int 4 \sin{\left(5 x - 4 \right)} \, dx
-4*cos(5*x - 4)/5
trigonometric
x
atom-0271
atomic
1
-tan(4*x + 5)
- \tan{\left(4 x + 5 \right)}
\int - \tan{\left(4 x + 5 \right)} \, dx
-log(tan(4*x + 5)**2 + 1)/8
trigonometric
x
atom-0272
atomic
1
cos(4*x + 1)
\cos{\left(4 x + 1 \right)}
\int \cos{\left(4 x + 1 \right)} \, dx
sin(4*x + 1)/4
trigonometric
x
atom-0273
atomic
1
-4*tan(2*x + 12)
- 4 \tan{\left(2 x + 12 \right)}
\int - 4 \tan{\left(2 x + 12 \right)} \, dx
-log(tan(2*x + 12)**2 + 1)
trigonometric
x
atom-0274
atomic
1
5*tan(5*x + 13)
5 \tan{\left(5 x + 13 \right)}
\int 5 \tan{\left(5 x + 13 \right)} \, dx
log(tan(5*x + 13)**2 + 1)/2
trigonometric
x
atom-0275
atomic
1
2*sin(2*x + 1)
2 \sin{\left(2 x + 1 \right)}
\int 2 \sin{\left(2 x + 1 \right)} \, dx
-cos(2*x + 1)
trigonometric
x
atom-0276
atomic
1
-2*tan(3*x + 2)
- 2 \tan{\left(3 x + 2 \right)}
\int - 2 \tan{\left(3 x + 2 \right)} \, dx
-log(tan(3*x + 2)**2 + 1)/3
trigonometric
x
atom-0277
atomic
1
cos(5*x - 6)
\cos{\left(5 x - 6 \right)}
\int \cos{\left(5 x - 6 \right)} \, dx
sin(5*x - 6)/5
trigonometric
x
atom-0278
atomic
1
-3*cos(6*x + 14)
- 3 \cos{\left(6 x + 14 \right)}
\int - 3 \cos{\left(6 x + 14 \right)} \, dx
-sin(6*x + 14)/2
trigonometric
x
atom-0279
atomic
1
4*sin(13*x + 2)
4 \sin{\left(13 x + 2 \right)}
\int 4 \sin{\left(13 x + 2 \right)} \, dx
-4*cos(13*x + 2)/13
trigonometric
x
atom-0280
atomic
1
-3*tan(2*x - 14)
- 3 \tan{\left(2 x - 14 \right)}
\int - 3 \tan{\left(2 x - 14 \right)} \, dx
-3*log(tan(2*x - 14)**2 + 1)/4
trigonometric
x
atom-0281
atomic
1
-3*sin(5*x - 6)
- 3 \sin{\left(5 x - 6 \right)}
\int - 3 \sin{\left(5 x - 6 \right)} \, dx
3*cos(5*x - 6)/5
trigonometric
x
atom-0282
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-0283
atomic
1
-5*tan(15*x - 6)
- 5 \tan{\left(15 x - 6 \right)}
\int - 5 \tan{\left(15 x - 6 \right)} \, dx
-log(tan(15*x - 6)**2 + 1)/6
trigonometric
x
atom-0284
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-0285
atomic
1
-2*sin(8*x - 12)
- 2 \sin{\left(8 x - 12 \right)}
\int - 2 \sin{\left(8 x - 12 \right)} \, dx
cos(8*x - 12)/4
trigonometric
x
atom-0286
atomic
1
3*cos(4*x + 12)
3 \cos{\left(4 x + 12 \right)}
\int 3 \cos{\left(4 x + 12 \right)} \, dx
3*sin(4*x + 12)/4
trigonometric
x
atom-0287
atomic
1
tan(12*x + 2)
\tan{\left(12 x + 2 \right)}
\int \tan{\left(12 x + 2 \right)} \, dx
log(tan(12*x + 2)**2 + 1)/24
trigonometric
x
atom-0288
atomic
1
5*tan(2*x - 15)
5 \tan{\left(2 x - 15 \right)}
\int 5 \tan{\left(2 x - 15 \right)} \, dx
5*log(tan(2*x - 15)**2 + 1)/4
trigonometric
x
atom-0289
atomic
1
-cos(15*x + 10)
- \cos{\left(15 x + 10 \right)}
\int - \cos{\left(15 x + 10 \right)} \, dx
-sin(15*x + 10)/15
trigonometric
x
atom-0290
atomic
1
-cos(14*x - 5)
- \cos{\left(14 x - 5 \right)}
\int - \cos{\left(14 x - 5 \right)} \, dx
-sin(14*x - 5)/14
trigonometric
x
atom-0291
atomic
1
-3*cos(3*x + 6)
- 3 \cos{\left(3 x + 6 \right)}
\int - 3 \cos{\left(3 x + 6 \right)} \, dx
-sin(3*x + 6)
trigonometric
x
atom-0292
atomic
1
-5*tan(15*x + 13)
- 5 \tan{\left(15 x + 13 \right)}
\int - 5 \tan{\left(15 x + 13 \right)} \, dx
-log(tan(15*x + 13)**2 + 1)/6
trigonometric
x
atom-0293
atomic
1
cos(2*x + 1)
\cos{\left(2 x + 1 \right)}
\int \cos{\left(2 x + 1 \right)} \, dx
sin(2*x + 1)/2
trigonometric
x
atom-0294
atomic
1
-tan(8*x - 5)
- \tan{\left(8 x - 5 \right)}
\int - \tan{\left(8 x - 5 \right)} \, dx
-log(tan(8*x - 5)**2 + 1)/16
trigonometric
x
atom-0295
atomic
1
5*tan(11*x + 10)
5 \tan{\left(11 x + 10 \right)}
\int 5 \tan{\left(11 x + 10 \right)} \, dx
5*log(tan(11*x + 10)**2 + 1)/22
trigonometric
x
atom-0296
atomic
1
4*tan(7*x + 1)
4 \tan{\left(7 x + 1 \right)}
\int 4 \tan{\left(7 x + 1 \right)} \, dx
2*log(tan(7*x + 1)**2 + 1)/7
trigonometric
x
atom-0297
atomic
1
4*cos(x + 2)
4 \cos{\left(x + 2 \right)}
\int 4 \cos{\left(x + 2 \right)} \, dx
4*sin(x + 2)
trigonometric
x
atom-0298
atomic
1
3*cos(12*x + 4)
3 \cos{\left(12 x + 4 \right)}
\int 3 \cos{\left(12 x + 4 \right)} \, dx
sin(12*x + 4)/4
trigonometric
x
atom-0299
atomic
1
5*cos(6*x + 3)
5 \cos{\left(6 x + 3 \right)}
\int 5 \cos{\left(6 x + 3 \right)} \, dx
5*sin(6*x + 3)/6
trigonometric
x