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-0600
atomic
1
4/(10 - 3*x)
\frac{4}{10 - 3 x}
\int \frac{4}{10 - 3 x} \, dx
-4*log(3*x - 10)/3
logarithmic_rational
x
atom-0601
atomic
1
1/(11*x + 11)
\frac{1}{11 x + 11}
\int \frac{1}{11 x + 11} \, dx
log(11*x + 11)/11
logarithmic_rational
x
atom-0602
atomic
1
-log(4 - 5*x)
- \log{\left(4 - 5 x \right)}
\int - \log{\left(4 - 5 x \right)} \, dx
-x*log(4 - 5*x) + x + 4*log(5*x - 4)/5
logarithmic_rational
x
atom-0603
atomic
1
2*log(-5*x - 10)
2 \log{\left(- 5 x - 10 \right)}
\int 2 \log{\left(- 5 x - 10 \right)} \, dx
2*x*log(-5*x - 10) - 2*x + 4*log(x + 2)
logarithmic_rational
x
atom-0604
atomic
1
-1/(8*x + 7)
- \frac{1}{8 x + 7}
\int - \frac{1}{8 x + 7} \, dx
-log(8*x + 7)/8
logarithmic_rational
x
atom-0605
atomic
1
log(11 - 7*x)
\log{\left(11 - 7 x \right)}
\int \log{\left(11 - 7 x \right)} \, dx
x*log(11 - 7*x) - x - 11*log(7*x - 11)/7
logarithmic_rational
x
atom-0606
atomic
1
-4/(14*x + 3)
- \frac{4}{14 x + 3}
\int - \frac{4}{14 x + 3} \, dx
-2*log(14*x + 3)/7
logarithmic_rational
x
atom-0607
atomic
1
5*log(9*x + 2)
5 \log{\left(9 x + 2 \right)}
\int 5 \log{\left(9 x + 2 \right)} \, dx
5*x*log(9*x + 2) - 5*x + 10*log(9*x + 2)/9
logarithmic_rational
x
atom-0608
atomic
1
-2/(10 - x)
- \frac{2}{10 - x}
\int - \frac{2}{10 - x} \, dx
2*log(x - 10)
logarithmic_rational
x
atom-0609
atomic
1
log(6*x)
\log{\left(6 x \right)}
\int \log{\left(6 x \right)} \, dx
x*log(6*x) - x
logarithmic_rational
x
atom-0610
atomic
1
-2/(6 - 7*x)
- \frac{2}{6 - 7 x}
\int - \frac{2}{6 - 7 x} \, dx
2*log(7*x - 6)/7
logarithmic_rational
x
atom-0611
atomic
1
1/(-13*x - 1)
\frac{1}{- 13 x - 1}
\int \frac{1}{- 13 x - 1} \, dx
-log(13*x + 1)/13
logarithmic_rational
x
atom-0612
atomic
1
4/(2 - 3*x)
\frac{4}{2 - 3 x}
\int \frac{4}{2 - 3 x} \, dx
-4*log(3*x - 2)/3
logarithmic_rational
x
atom-0613
atomic
1
3/(10 - 14*x)
\frac{3}{10 - 14 x}
\int \frac{3}{10 - 14 x} \, dx
-3*log(14*x - 10)/14
logarithmic_rational
x
atom-0614
atomic
1
-4*log(9*x - 8)
- 4 \log{\left(9 x - 8 \right)}
\int - 4 \log{\left(9 x - 8 \right)} \, dx
-4*x*log(9*x - 8) + 4*x + 32*log(9*x - 8)/9
logarithmic_rational
x
atom-0615
atomic
1
-3/(5*x + 4)
- \frac{3}{5 x + 4}
\int - \frac{3}{5 x + 4} \, dx
-3*log(5*x + 4)/5
logarithmic_rational
x
atom-0616
atomic
1
1/(-12*x - 15)
\frac{1}{- 12 x - 15}
\int \frac{1}{- 12 x - 15} \, dx
-log(12*x + 15)/12
logarithmic_rational
x
atom-0617
atomic
1
3*log(8*x + 1)
3 \log{\left(8 x + 1 \right)}
\int 3 \log{\left(8 x + 1 \right)} \, dx
3*x*log(8*x + 1) - 3*x + 3*log(8*x + 1)/8
logarithmic_rational
x
atom-0618
atomic
1
2*log(-4*x - 3)
2 \log{\left(- 4 x - 3 \right)}
\int 2 \log{\left(- 4 x - 3 \right)} \, dx
2*x*log(-4*x - 3) - 2*x + 3*log(4*x + 3)/2
logarithmic_rational
x
atom-0619
atomic
1
-5*log(-12*x - 6)
- 5 \log{\left(- 12 x - 6 \right)}
\int - 5 \log{\left(- 12 x - 6 \right)} \, dx
-5*x*log(-12*x - 6) + 5*x - 5*log(2*x + 1)/2
logarithmic_rational
x
atom-0620
atomic
1
-4*log(11*x + 15)
- 4 \log{\left(11 x + 15 \right)}
\int - 4 \log{\left(11 x + 15 \right)} \, dx
-4*x*log(11*x + 15) + 4*x - 60*log(11*x + 15)/11
logarithmic_rational
x
atom-0621
atomic
1
-1/(-5*x - 1)
- \frac{1}{- 5 x - 1}
\int - \frac{1}{- 5 x - 1} \, dx
log(5*x + 1)/5
logarithmic_rational
x
atom-0622
atomic
1
2/(-12*x - 1)
\frac{2}{- 12 x - 1}
\int \frac{2}{- 12 x - 1} \, dx
-log(12*x + 1)/6
logarithmic_rational
x
atom-0623
atomic
1
-4/(-6*x - 14)
- \frac{4}{- 6 x - 14}
\int - \frac{4}{- 6 x - 14} \, dx
2*log(3*x + 7)/3
logarithmic_rational
x
atom-0624
atomic
1
-5*log(12*x - 5)
- 5 \log{\left(12 x - 5 \right)}
\int - 5 \log{\left(12 x - 5 \right)} \, dx
-5*x*log(12*x - 5) + 5*x + 25*log(12*x - 5)/12
logarithmic_rational
x
atom-0625
atomic
1
-2*log(x - 10)
- 2 \log{\left(x - 10 \right)}
\int - 2 \log{\left(x - 10 \right)} \, dx
-2*x*log(x - 10) + 2*x + 20*log(x - 10)
logarithmic_rational
x
atom-0626
atomic
1
3/(15 - 2*x)
\frac{3}{15 - 2 x}
\int \frac{3}{15 - 2 x} \, dx
-3*log(2*x - 15)/2
logarithmic_rational
x
atom-0627
atomic
1
5/(-10*x - 10)
\frac{5}{- 10 x - 10}
\int \frac{5}{- 10 x - 10} \, dx
-log(2*x + 2)/2
logarithmic_rational
x
atom-0628
atomic
1
1/(8 - 15*x)
\frac{1}{8 - 15 x}
\int \frac{1}{8 - 15 x} \, dx
-log(15*x - 8)/15
logarithmic_rational
x
atom-0629
atomic
1
2*log(3*x - 2)
2 \log{\left(3 x - 2 \right)}
\int 2 \log{\left(3 x - 2 \right)} \, dx
2*x*log(3*x - 2) - 2*x - 4*log(3*x - 2)/3
logarithmic_rational
x
atom-0630
atomic
1
-2*log(9 - 7*x)
- 2 \log{\left(9 - 7 x \right)}
\int - 2 \log{\left(9 - 7 x \right)} \, dx
-2*x*log(9 - 7*x) + 2*x + 18*log(7*x - 9)/7
logarithmic_rational
x
atom-0631
atomic
1
4*log(10 - 12*x)
4 \log{\left(10 - 12 x \right)}
\int 4 \log{\left(10 - 12 x \right)} \, dx
4*x*log(10 - 12*x) - 4*x - 10*log(6*x - 5)/3
logarithmic_rational
x
atom-0632
atomic
1
-2*log(-x - 12)
- 2 \log{\left(- x - 12 \right)}
\int - 2 \log{\left(- x - 12 \right)} \, dx
-2*x*log(-x - 12) + 2*x - 24*log(x + 12)
logarithmic_rational
x
atom-0633
atomic
1
3/(15*x + 5)
\frac{3}{15 x + 5}
\int \frac{3}{15 x + 5} \, dx
log(15*x + 5)/5
logarithmic_rational
x
atom-0634
atomic
1
4/(3 - 3*x)
\frac{4}{3 - 3 x}
\int \frac{4}{3 - 3 x} \, dx
-4*log(3*x - 3)/3
logarithmic_rational
x
atom-0635
atomic
1
2/(4*x - 10)
\frac{2}{4 x - 10}
\int \frac{2}{4 x - 10} \, dx
log(2*x - 5)/2
logarithmic_rational
x
atom-0636
atomic
1
4/(3*x - 13)
\frac{4}{3 x - 13}
\int \frac{4}{3 x - 13} \, dx
4*log(3*x - 13)/3
logarithmic_rational
x
atom-0637
atomic
1
-4/(-8*x - 6)
- \frac{4}{- 8 x - 6}
\int - \frac{4}{- 8 x - 6} \, dx
log(4*x + 3)/2
logarithmic_rational
x
atom-0638
atomic
1
-3/(x - 3)
- \frac{3}{x - 3}
\int - \frac{3}{x - 3} \, dx
-3*log(x - 3)
logarithmic_rational
x
atom-0639
atomic
1
4*log(-3*x - 2)
4 \log{\left(- 3 x - 2 \right)}
\int 4 \log{\left(- 3 x - 2 \right)} \, dx
4*x*log(-3*x - 2) - 4*x + 8*log(3*x + 2)/3
logarithmic_rational
x
atom-0640
atomic
1
3*log(-10*x)
3 \log{\left(- 10 x \right)}
\int 3 \log{\left(- 10 x \right)} \, dx
3*x*log(-10*x) - 3*x
logarithmic_rational
x
atom-0641
atomic
1
2*log(4*x - 14)
2 \log{\left(4 x - 14 \right)}
\int 2 \log{\left(4 x - 14 \right)} \, dx
2*x*log(4*x - 14) - 2*x - 7*log(2*x - 7)
logarithmic_rational
x
atom-0642
atomic
1
2*log(-11*x - 9)
2 \log{\left(- 11 x - 9 \right)}
\int 2 \log{\left(- 11 x - 9 \right)} \, dx
2*x*log(-11*x - 9) - 2*x + 18*log(11*x + 9)/11
logarithmic_rational
x
atom-0643
atomic
1
1/(6*x)
\frac{1}{6 x}
\int \frac{1}{6 x} \, dx
log(x)/6
logarithmic_rational
x
atom-0644
atomic
1
2/(-10*x - 13)
\frac{2}{- 10 x - 13}
\int \frac{2}{- 10 x - 13} \, dx
-log(10*x + 13)/5
logarithmic_rational
x
atom-0645
atomic
1
-log(-14*x - 7)
- \log{\left(- 14 x - 7 \right)}
\int - \log{\left(- 14 x - 7 \right)} \, dx
-x*log(-14*x - 7) + x - log(2*x + 1)/2
logarithmic_rational
x
atom-0646
atomic
1
-3/(9*x - 1)
- \frac{3}{9 x - 1}
\int - \frac{3}{9 x - 1} \, dx
-log(9*x - 1)/3
logarithmic_rational
x
atom-0647
atomic
1
3/(x - 12)
\frac{3}{x - 12}
\int \frac{3}{x - 12} \, dx
3*log(x - 12)
logarithmic_rational
x
atom-0648
atomic
1
3/(11*x - 4)
\frac{3}{11 x - 4}
\int \frac{3}{11 x - 4} \, dx
3*log(11*x - 4)/11
logarithmic_rational
x
atom-0649
atomic
1
2*log(2*x - 9)
2 \log{\left(2 x - 9 \right)}
\int 2 \log{\left(2 x - 9 \right)} \, dx
2*x*log(2*x - 9) - 2*x - 9*log(2*x - 9)
logarithmic_rational
x
atom-0650
atomic
1
5*log(9*x - 8)
5 \log{\left(9 x - 8 \right)}
\int 5 \log{\left(9 x - 8 \right)} \, dx
5*x*log(9*x - 8) - 5*x - 40*log(9*x - 8)/9
logarithmic_rational
x
atom-0651
atomic
1
2*log(-7*x - 4)
2 \log{\left(- 7 x - 4 \right)}
\int 2 \log{\left(- 7 x - 4 \right)} \, dx
2*x*log(-7*x - 4) - 2*x + 8*log(7*x + 4)/7
logarithmic_rational
x
atom-0652
atomic
1
2*log(12*x - 12)
2 \log{\left(12 x - 12 \right)}
\int 2 \log{\left(12 x - 12 \right)} \, dx
2*x*log(12*x - 12) - 2*x - 2*log(x - 1)
logarithmic_rational
x
atom-0653
atomic
1
-2*log(10*x + 8)
- 2 \log{\left(10 x + 8 \right)}
\int - 2 \log{\left(10 x + 8 \right)} \, dx
-2*x*log(10*x + 8) + 2*x - 8*log(5*x + 4)/5
logarithmic_rational
x
atom-0654
atomic
1
4/(5*x - 2)
\frac{4}{5 x - 2}
\int \frac{4}{5 x - 2} \, dx
4*log(5*x - 2)/5
logarithmic_rational
x
atom-0655
atomic
1
-2*log(11*x - 9)
- 2 \log{\left(11 x - 9 \right)}
\int - 2 \log{\left(11 x - 9 \right)} \, dx
-2*x*log(11*x - 9) + 2*x + 18*log(11*x - 9)/11
logarithmic_rational
x
atom-0656
atomic
1
3/(4 - 7*x)
\frac{3}{4 - 7 x}
\int \frac{3}{4 - 7 x} \, dx
-3*log(7*x - 4)/7
logarithmic_rational
x
atom-0657
atomic
1
-1/(3 - 6*x)
- \frac{1}{3 - 6 x}
\int - \frac{1}{3 - 6 x} \, dx
log(6*x - 3)/6
logarithmic_rational
x
atom-0658
atomic
1
-3*log(15*x + 9)
- 3 \log{\left(15 x + 9 \right)}
\int - 3 \log{\left(15 x + 9 \right)} \, dx
-3*x*log(15*x + 9) + 3*x - 9*log(5*x + 3)/5
logarithmic_rational
x
atom-0659
atomic
1
-log(12*x + 5)
- \log{\left(12 x + 5 \right)}
\int - \log{\left(12 x + 5 \right)} \, dx
-x*log(12*x + 5) + x - 5*log(12*x + 5)/12
logarithmic_rational
x
atom-0660
atomic
1
-2*log(7 - 11*x)
- 2 \log{\left(7 - 11 x \right)}
\int - 2 \log{\left(7 - 11 x \right)} \, dx
-2*x*log(7 - 11*x) + 2*x + 14*log(11*x - 7)/11
logarithmic_rational
x
atom-0661
atomic
1
5*log(-3*x)
5 \log{\left(- 3 x \right)}
\int 5 \log{\left(- 3 x \right)} \, dx
5*x*log(-3*x) - 5*x
logarithmic_rational
x
atom-0662
atomic
1
5/(-2*x - 3)
\frac{5}{- 2 x - 3}
\int \frac{5}{- 2 x - 3} \, dx
-5*log(2*x + 3)/2
logarithmic_rational
x
atom-0663
atomic
1
log(x + 8)
\log{\left(x + 8 \right)}
\int \log{\left(x + 8 \right)} \, dx
x*log(x + 8) - x + 8*log(x + 8)
logarithmic_rational
x
atom-0664
atomic
1
2/(15*x)
\frac{2}{15 x}
\int \frac{2}{15 x} \, dx
2*log(x)/15
logarithmic_rational
x
atom-0665
atomic
1
-4*log(8*x - 1)
- 4 \log{\left(8 x - 1 \right)}
\int - 4 \log{\left(8 x - 1 \right)} \, dx
-4*x*log(8*x - 1) + 4*x + log(8*x - 1)/2
logarithmic_rational
x
atom-0666
atomic
1
-4/(10*x + 2)
- \frac{4}{10 x + 2}
\int - \frac{4}{10 x + 2} \, dx
-2*log(5*x + 1)/5
logarithmic_rational
x
atom-0667
atomic
1
-2/(-7*x - 5)
- \frac{2}{- 7 x - 5}
\int - \frac{2}{- 7 x - 5} \, dx
2*log(7*x + 5)/7
logarithmic_rational
x
atom-0668
atomic
1
3/(3*x - 11)
\frac{3}{3 x - 11}
\int \frac{3}{3 x - 11} \, dx
log(3*x - 11)
logarithmic_rational
x
atom-0669
atomic
1
5/(9*x - 14)
\frac{5}{9 x - 14}
\int \frac{5}{9 x - 14} \, dx
5*log(9*x - 14)/9
logarithmic_rational
x
atom-0670
atomic
1
-5/(14 - 12*x)
- \frac{5}{14 - 12 x}
\int - \frac{5}{14 - 12 x} \, dx
5*log(12*x - 14)/12
logarithmic_rational
x
atom-0671
atomic
1
2/(15 - 15*x)
\frac{2}{15 - 15 x}
\int \frac{2}{15 - 15 x} \, dx
-2*log(15*x - 15)/15
logarithmic_rational
x
atom-0672
atomic
1
5*log(-6*x - 10)
5 \log{\left(- 6 x - 10 \right)}
\int 5 \log{\left(- 6 x - 10 \right)} \, dx
5*x*log(-6*x - 10) - 5*x + 25*log(3*x + 5)/3
logarithmic_rational
x
atom-0673
atomic
1
-4/(5*x - 4)
- \frac{4}{5 x - 4}
\int - \frac{4}{5 x - 4} \, dx
-4*log(5*x - 4)/5
logarithmic_rational
x
atom-0674
atomic
1
5/(13*x + 5)
\frac{5}{13 x + 5}
\int \frac{5}{13 x + 5} \, dx
5*log(13*x + 5)/13
logarithmic_rational
x
atom-0675
atomic
1
5/(8 - 6*x)
\frac{5}{8 - 6 x}
\int \frac{5}{8 - 6 x} \, dx
-5*log(6*x - 8)/6
logarithmic_rational
x
atom-0676
atomic
1
log(5*x - 13)
\log{\left(5 x - 13 \right)}
\int \log{\left(5 x - 13 \right)} \, dx
x*log(5*x - 13) - x - 13*log(5*x - 13)/5
logarithmic_rational
x
atom-0677
atomic
1
-2*log(-13*x - 11)
- 2 \log{\left(- 13 x - 11 \right)}
\int - 2 \log{\left(- 13 x - 11 \right)} \, dx
-2*x*log(-13*x - 11) + 2*x - 22*log(13*x + 11)/13
logarithmic_rational
x
atom-0678
atomic
1
-5/(7 - 15*x)
- \frac{5}{7 - 15 x}
\int - \frac{5}{7 - 15 x} \, dx
log(15*x - 7)/3
logarithmic_rational
x
atom-0679
atomic
1
log(7*x - 11)
\log{\left(7 x - 11 \right)}
\int \log{\left(7 x - 11 \right)} \, dx
x*log(7*x - 11) - x - 11*log(7*x - 11)/7
logarithmic_rational
x
atom-0680
atomic
1
log(8 - 13*x)
\log{\left(8 - 13 x \right)}
\int \log{\left(8 - 13 x \right)} \, dx
x*log(8 - 13*x) - x - 8*log(13*x - 8)/13
logarithmic_rational
x
atom-0681
atomic
1
-log(-11*x - 3)
- \log{\left(- 11 x - 3 \right)}
\int - \log{\left(- 11 x - 3 \right)} \, dx
-x*log(-11*x - 3) + x - 3*log(11*x + 3)/11
logarithmic_rational
x
atom-0682
atomic
1
5*log(6*x - 11)
5 \log{\left(6 x - 11 \right)}
\int 5 \log{\left(6 x - 11 \right)} \, dx
5*x*log(6*x - 11) - 5*x - 55*log(6*x - 11)/6
logarithmic_rational
x
atom-0683
atomic
1
4*log(5*x - 10)
4 \log{\left(5 x - 10 \right)}
\int 4 \log{\left(5 x - 10 \right)} \, dx
4*x*log(5*x - 10) - 4*x - 8*log(x - 2)
logarithmic_rational
x
atom-0684
atomic
1
5*log(8*x - 11)
5 \log{\left(8 x - 11 \right)}
\int 5 \log{\left(8 x - 11 \right)} \, dx
5*x*log(8*x - 11) - 5*x - 55*log(8*x - 11)/8
logarithmic_rational
x
atom-0685
atomic
1
-2/(13 - 13*x)
- \frac{2}{13 - 13 x}
\int - \frac{2}{13 - 13 x} \, dx
2*log(13*x - 13)/13
logarithmic_rational
x
atom-0686
atomic
1
4*log(8*x - 3)
4 \log{\left(8 x - 3 \right)}
\int 4 \log{\left(8 x - 3 \right)} \, dx
4*x*log(8*x - 3) - 4*x - 3*log(8*x - 3)/2
logarithmic_rational
x
atom-0687
atomic
1
-3/(-8*x - 7)
- \frac{3}{- 8 x - 7}
\int - \frac{3}{- 8 x - 7} \, dx
3*log(8*x + 7)/8
logarithmic_rational
x
atom-0688
atomic
1
3*log(4*x + 4)
3 \log{\left(4 x + 4 \right)}
\int 3 \log{\left(4 x + 4 \right)} \, dx
3*x*log(4*x + 4) - 3*x + 3*log(x + 1)
logarithmic_rational
x
atom-0689
atomic
1
-5/(12*x + 12)
- \frac{5}{12 x + 12}
\int - \frac{5}{12 x + 12} \, dx
-5*log(12*x + 12)/12
logarithmic_rational
x
atom-0690
atomic
1
-2/(x + 4)
- \frac{2}{x + 4}
\int - \frac{2}{x + 4} \, dx
-2*log(x + 4)
logarithmic_rational
x
atom-0691
atomic
1
-1/(5*x - 14)
- \frac{1}{5 x - 14}
\int - \frac{1}{5 x - 14} \, dx
-log(5*x - 14)/5
logarithmic_rational
x
atom-0692
atomic
1
2*log(-3*x - 12)
2 \log{\left(- 3 x - 12 \right)}
\int 2 \log{\left(- 3 x - 12 \right)} \, dx
2*x*log(-3*x - 12) - 2*x + 8*log(x + 4)
logarithmic_rational
x
atom-0693
atomic
1
3*log(13*x - 15)
3 \log{\left(13 x - 15 \right)}
\int 3 \log{\left(13 x - 15 \right)} \, dx
3*x*log(13*x - 15) - 3*x - 45*log(13*x - 15)/13
logarithmic_rational
x
atom-0694
atomic
1
-3/(12 - 3*x)
- \frac{3}{12 - 3 x}
\int - \frac{3}{12 - 3 x} \, dx
log(x - 4)
logarithmic_rational
x
atom-0695
atomic
1
3/(6*x - 10)
\frac{3}{6 x - 10}
\int \frac{3}{6 x - 10} \, dx
log(6*x - 10)/2
logarithmic_rational
x
atom-0696
atomic
1
-5*log(3*x - 13)
- 5 \log{\left(3 x - 13 \right)}
\int - 5 \log{\left(3 x - 13 \right)} \, dx
-5*x*log(3*x - 13) + 5*x + 65*log(3*x - 13)/3
logarithmic_rational
x
atom-0697
atomic
1
-5*log(14*x - 14)
- 5 \log{\left(14 x - 14 \right)}
\int - 5 \log{\left(14 x - 14 \right)} \, dx
-5*x*log(14*x - 14) + 5*x + 5*log(x - 1)
logarithmic_rational
x
atom-0698
atomic
1
3/(5 - 6*x)
\frac{3}{5 - 6 x}
\int \frac{3}{5 - 6 x} \, dx
-log(6*x - 5)/2
logarithmic_rational
x
atom-0699
atomic
1
1/(7*x - 3)
\frac{1}{7 x - 3}
\int \frac{1}{7 x - 3} \, dx
log(7*x - 3)/7
logarithmic_rational
x