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-0500 | atomic | 1 | -exp(-5*x) | - e^{- 5 x} | \int - e^{- 5 x} \, dx | exp(-5*x)/5 | exponential | x |
atom-0501 | atomic | 1 | -5*exp(14*x) | - 5 e^{14 x} | \int - 5 e^{14 x} \, dx | -5*exp(14*x)/14 | exponential | x |
atom-0502 | atomic | 1 | 5*exp(3*x) | 5 e^{3 x} | \int 5 e^{3 x} \, dx | 5*exp(3*x)/3 | exponential | x |
atom-0503 | atomic | 1 | exp(13*x) | e^{13 x} | \int e^{13 x} \, dx | exp(13*x)/13 | exponential | x |
atom-0504 | atomic | 1 | 2*exp(-10*x) | 2 e^{- 10 x} | \int 2 e^{- 10 x} \, dx | -exp(-10*x)/5 | exponential | x |
atom-0505 | atomic | 1 | -exp(13*x) | - e^{13 x} | \int - e^{13 x} \, dx | -exp(13*x)/13 | exponential | x |
atom-0506 | atomic | 1 | -exp(3*x) | - e^{3 x} | \int - e^{3 x} \, dx | -exp(3*x)/3 | exponential | x |
atom-0507 | atomic | 1 | -exp(-x) | - e^{- x} | \int - e^{- x} \, dx | exp(-x) | exponential | x |
atom-0508 | atomic | 1 | 3*exp(x) | 3 e^{x} | \int 3 e^{x} \, dx | 3*exp(x) | exponential | x |
atom-0509 | atomic | 1 | -3*exp(12*x) | - 3 e^{12 x} | \int - 3 e^{12 x} \, dx | -exp(12*x)/4 | exponential | x |
atom-0510 | atomic | 1 | -exp(-9*x) | - e^{- 9 x} | \int - e^{- 9 x} \, dx | exp(-9*x)/9 | exponential | x |
atom-0511 | atomic | 1 | -3*exp(8*x) | - 3 e^{8 x} | \int - 3 e^{8 x} \, dx | -3*exp(8*x)/8 | exponential | x |
atom-0512 | atomic | 1 | -2*exp(-10*x) | - 2 e^{- 10 x} | \int - 2 e^{- 10 x} \, dx | exp(-10*x)/5 | exponential | x |
atom-0513 | atomic | 1 | exp(6*x) | e^{6 x} | \int e^{6 x} \, dx | exp(6*x)/6 | exponential | x |
atom-0514 | atomic | 1 | -5*exp(-7*x) | - 5 e^{- 7 x} | \int - 5 e^{- 7 x} \, dx | 5*exp(-7*x)/7 | exponential | x |
atom-0515 | atomic | 1 | 2*exp(9*x) | 2 e^{9 x} | \int 2 e^{9 x} \, dx | 2*exp(9*x)/9 | exponential | x |
atom-0516 | atomic | 1 | 2*exp(-6*x) | 2 e^{- 6 x} | \int 2 e^{- 6 x} \, dx | -exp(-6*x)/3 | exponential | x |
atom-0517 | atomic | 1 | -exp(-4*x) | - e^{- 4 x} | \int - e^{- 4 x} \, dx | exp(-4*x)/4 | exponential | x |
atom-0518 | atomic | 1 | 3*exp(14*x) | 3 e^{14 x} | \int 3 e^{14 x} \, dx | 3*exp(14*x)/14 | exponential | x |
atom-0519 | atomic | 1 | 3*exp(10*x) | 3 e^{10 x} | \int 3 e^{10 x} \, dx | 3*exp(10*x)/10 | exponential | x |
atom-0520 | atomic | 1 | -2*exp(9*x) | - 2 e^{9 x} | \int - 2 e^{9 x} \, dx | -2*exp(9*x)/9 | exponential | x |
atom-0521 | atomic | 1 | 4*exp(12*x) | 4 e^{12 x} | \int 4 e^{12 x} \, dx | exp(12*x)/3 | exponential | x |
atom-0522 | atomic | 1 | -4*exp(14*x) | - 4 e^{14 x} | \int - 4 e^{14 x} \, dx | -2*exp(14*x)/7 | exponential | x |
atom-0523 | atomic | 1 | 3*exp(-9*x) | 3 e^{- 9 x} | \int 3 e^{- 9 x} \, dx | -exp(-9*x)/3 | exponential | x |
atom-0524 | atomic | 1 | -3*exp(-10*x) | - 3 e^{- 10 x} | \int - 3 e^{- 10 x} \, dx | 3*exp(-10*x)/10 | exponential | x |
atom-0525 | atomic | 1 | -4*exp(13*x) | - 4 e^{13 x} | \int - 4 e^{13 x} \, dx | -4*exp(13*x)/13 | exponential | x |
atom-0526 | atomic | 1 | -5*exp(-x) | - 5 e^{- x} | \int - 5 e^{- x} \, dx | 5*exp(-x) | exponential | x |
atom-0527 | atomic | 1 | exp(-x) | e^{- x} | \int e^{- x} \, dx | -exp(-x) | exponential | x |
atom-0528 | atomic | 1 | -2*exp(3*x) | - 2 e^{3 x} | \int - 2 e^{3 x} \, dx | -2*exp(3*x)/3 | exponential | x |
atom-0529 | atomic | 1 | 3*exp(-14*x) | 3 e^{- 14 x} | \int 3 e^{- 14 x} \, dx | -3*exp(-14*x)/14 | exponential | x |
atom-0530 | atomic | 1 | -exp(-2*x) | - e^{- 2 x} | \int - e^{- 2 x} \, dx | exp(-2*x)/2 | exponential | x |
atom-0531 | atomic | 1 | -3*exp(9*x) | - 3 e^{9 x} | \int - 3 e^{9 x} \, dx | -exp(9*x)/3 | exponential | x |
atom-0532 | atomic | 1 | 5*exp(15*x) | 5 e^{15 x} | \int 5 e^{15 x} \, dx | exp(15*x)/3 | exponential | x |
atom-0533 | atomic | 1 | exp(-3*x) | e^{- 3 x} | \int e^{- 3 x} \, dx | -exp(-3*x)/3 | exponential | x |
atom-0534 | atomic | 1 | 5*exp(12*x) | 5 e^{12 x} | \int 5 e^{12 x} \, dx | 5*exp(12*x)/12 | exponential | x |
atom-0535 | atomic | 1 | -3*exp(2*x) | - 3 e^{2 x} | \int - 3 e^{2 x} \, dx | -3*exp(2*x)/2 | exponential | x |
atom-0536 | atomic | 1 | -5*exp(9*x) | - 5 e^{9 x} | \int - 5 e^{9 x} \, dx | -5*exp(9*x)/9 | exponential | x |
atom-0537 | atomic | 1 | 3*exp(-2*x) | 3 e^{- 2 x} | \int 3 e^{- 2 x} \, dx | -3*exp(-2*x)/2 | exponential | x |
atom-0538 | atomic | 1 | -2*exp(-8*x) | - 2 e^{- 8 x} | \int - 2 e^{- 8 x} \, dx | exp(-8*x)/4 | exponential | x |
atom-0539 | atomic | 1 | -3*exp(-7*x) | - 3 e^{- 7 x} | \int - 3 e^{- 7 x} \, dx | 3*exp(-7*x)/7 | exponential | x |
atom-0540 | atomic | 1 | -4*exp(-14*x) | - 4 e^{- 14 x} | \int - 4 e^{- 14 x} \, dx | 2*exp(-14*x)/7 | exponential | x |
atom-0541 | atomic | 1 | -5*exp(-8*x) | - 5 e^{- 8 x} | \int - 5 e^{- 8 x} \, dx | 5*exp(-8*x)/8 | exponential | x |
atom-0542 | atomic | 1 | -4*exp(4*x) | - 4 e^{4 x} | \int - 4 e^{4 x} \, dx | -exp(4*x) | exponential | x |
atom-0543 | atomic | 1 | 4*exp(6*x) | 4 e^{6 x} | \int 4 e^{6 x} \, dx | 2*exp(6*x)/3 | exponential | x |
atom-0544 | atomic | 1 | -exp(-8*x) | - e^{- 8 x} | \int - e^{- 8 x} \, dx | exp(-8*x)/8 | exponential | x |
atom-0545 | atomic | 1 | 5*exp(11*x) | 5 e^{11 x} | \int 5 e^{11 x} \, dx | 5*exp(11*x)/11 | exponential | x |
atom-0546 | atomic | 1 | -exp(-7*x) | - e^{- 7 x} | \int - e^{- 7 x} \, dx | exp(-7*x)/7 | exponential | x |
atom-0547 | atomic | 1 | -3*exp(5*x) | - 3 e^{5 x} | \int - 3 e^{5 x} \, dx | -3*exp(5*x)/5 | exponential | x |
atom-0548 | atomic | 1 | 5*exp(6*x) | 5 e^{6 x} | \int 5 e^{6 x} \, dx | 5*exp(6*x)/6 | exponential | x |
atom-0549 | atomic | 1 | 3*exp(-5*x) | 3 e^{- 5 x} | \int 3 e^{- 5 x} \, dx | -3*exp(-5*x)/5 | exponential | x |
atom-0550 | atomic | 1 | -2*exp(12*x) | - 2 e^{12 x} | \int - 2 e^{12 x} \, dx | -exp(12*x)/6 | exponential | x |
atom-0551 | atomic | 1 | -3*exp(10*x) | - 3 e^{10 x} | \int - 3 e^{10 x} \, dx | -3*exp(10*x)/10 | exponential | x |
atom-0552 | atomic | 1 | -5*exp(2*x) | - 5 e^{2 x} | \int - 5 e^{2 x} \, dx | -5*exp(2*x)/2 | exponential | x |
atom-0553 | atomic | 1 | exp(2*x) | e^{2 x} | \int e^{2 x} \, dx | exp(2*x)/2 | exponential | x |
atom-0554 | atomic | 1 | exp(-8*x) | e^{- 8 x} | \int e^{- 8 x} \, dx | -exp(-8*x)/8 | exponential | x |
atom-0555 | atomic | 1 | 5*exp(-13*x) | 5 e^{- 13 x} | \int 5 e^{- 13 x} \, dx | -5*exp(-13*x)/13 | exponential | x |
atom-0556 | atomic | 1 | -4*exp(2*x) | - 4 e^{2 x} | \int - 4 e^{2 x} \, dx | -2*exp(2*x) | exponential | x |
atom-0557 | atomic | 1 | -2*exp(14*x) | - 2 e^{14 x} | \int - 2 e^{14 x} \, dx | -exp(14*x)/7 | exponential | x |
atom-0558 | atomic | 1 | -4*exp(8*x) | - 4 e^{8 x} | \int - 4 e^{8 x} \, dx | -exp(8*x)/2 | exponential | x |
atom-0559 | atomic | 1 | 2*exp(14*x) | 2 e^{14 x} | \int 2 e^{14 x} \, dx | exp(14*x)/7 | exponential | x |
atom-0560 | atomic | 1 | 4*exp(7*x) | 4 e^{7 x} | \int 4 e^{7 x} \, dx | 4*exp(7*x)/7 | exponential | x |
atom-0561 | atomic | 1 | -exp(-3*x) | - e^{- 3 x} | \int - e^{- 3 x} \, dx | exp(-3*x)/3 | exponential | x |
atom-0562 | atomic | 1 | -4*exp(10*x) | - 4 e^{10 x} | \int - 4 e^{10 x} \, dx | -2*exp(10*x)/5 | exponential | x |
atom-0563 | atomic | 1 | -3*exp(-15*x) | - 3 e^{- 15 x} | \int - 3 e^{- 15 x} \, dx | exp(-15*x)/5 | exponential | x |
atom-0564 | atomic | 1 | -2*exp(-3*x) | - 2 e^{- 3 x} | \int - 2 e^{- 3 x} \, dx | 2*exp(-3*x)/3 | exponential | x |
atom-0565 | atomic | 1 | 5*exp(-5*x) | 5 e^{- 5 x} | \int 5 e^{- 5 x} \, dx | -exp(-5*x) | exponential | x |
atom-0566 | atomic | 1 | 2*exp(15*x) | 2 e^{15 x} | \int 2 e^{15 x} \, dx | 2*exp(15*x)/15 | exponential | x |
atom-0567 | atomic | 1 | -3*exp(-11*x) | - 3 e^{- 11 x} | \int - 3 e^{- 11 x} \, dx | 3*exp(-11*x)/11 | exponential | x |
atom-0568 | atomic | 1 | -4*exp(15*x) | - 4 e^{15 x} | \int - 4 e^{15 x} \, dx | -4*exp(15*x)/15 | exponential | x |
atom-0569 | atomic | 1 | -2*exp(x) | - 2 e^{x} | \int - 2 e^{x} \, dx | -2*exp(x) | exponential | x |
atom-0570 | atomic | 1 | -5*exp(4*x) | - 5 e^{4 x} | \int - 5 e^{4 x} \, dx | -5*exp(4*x)/4 | exponential | x |
atom-0571 | atomic | 1 | 3*exp(8*x) | 3 e^{8 x} | \int 3 e^{8 x} \, dx | 3*exp(8*x)/8 | exponential | x |
atom-0572 | atomic | 1 | 5*exp(-2*x) | 5 e^{- 2 x} | \int 5 e^{- 2 x} \, dx | -5*exp(-2*x)/2 | exponential | x |
atom-0573 | atomic | 1 | -3*exp(-12*x) | - 3 e^{- 12 x} | \int - 3 e^{- 12 x} \, dx | exp(-12*x)/4 | exponential | x |
atom-0574 | atomic | 1 | 4*exp(x) | 4 e^{x} | \int 4 e^{x} \, dx | 4*exp(x) | exponential | x |
atom-0575 | atomic | 1 | -exp(10*x) | - e^{10 x} | \int - e^{10 x} \, dx | -exp(10*x)/10 | exponential | x |
atom-0576 | atomic | 1 | -2*exp(-6*x) | - 2 e^{- 6 x} | \int - 2 e^{- 6 x} \, dx | exp(-6*x)/3 | exponential | x |
atom-0577 | atomic | 1 | -4*exp(5*x) | - 4 e^{5 x} | \int - 4 e^{5 x} \, dx | -4*exp(5*x)/5 | exponential | x |
atom-0578 | atomic | 1 | 2*exp(-14*x) | 2 e^{- 14 x} | \int 2 e^{- 14 x} \, dx | -exp(-14*x)/7 | exponential | x |
atom-0579 | atomic | 1 | -3*exp(-13*x) | - 3 e^{- 13 x} | \int - 3 e^{- 13 x} \, dx | 3*exp(-13*x)/13 | exponential | x |
atom-0580 | atomic | 1 | exp(5*x) | e^{5 x} | \int e^{5 x} \, dx | exp(5*x)/5 | exponential | x |
atom-0581 | atomic | 1 | -2*exp(13*x) | - 2 e^{13 x} | \int - 2 e^{13 x} \, dx | -2*exp(13*x)/13 | exponential | x |
atom-0582 | atomic | 1 | 4*exp(-7*x) | 4 e^{- 7 x} | \int 4 e^{- 7 x} \, dx | -4*exp(-7*x)/7 | exponential | x |
atom-0583 | atomic | 1 | 3*exp(3*x) | 3 e^{3 x} | \int 3 e^{3 x} \, dx | exp(3*x) | exponential | x |
atom-0584 | atomic | 1 | -3*exp(14*x) | - 3 e^{14 x} | \int - 3 e^{14 x} \, dx | -3*exp(14*x)/14 | exponential | x |
atom-0585 | atomic | 1 | exp(14*x) | e^{14 x} | \int e^{14 x} \, dx | exp(14*x)/14 | exponential | x |
atom-0586 | atomic | 1 | -3*exp(3*x) | - 3 e^{3 x} | \int - 3 e^{3 x} \, dx | -exp(3*x) | exponential | x |
atom-0587 | atomic | 1 | exp(9*x) | e^{9 x} | \int e^{9 x} \, dx | exp(9*x)/9 | exponential | x |
atom-0588 | atomic | 1 | -4*exp(x) | - 4 e^{x} | \int - 4 e^{x} \, dx | -4*exp(x) | exponential | x |
atom-0589 | atomic | 1 | -5*exp(-12*x) | - 5 e^{- 12 x} | \int - 5 e^{- 12 x} \, dx | 5*exp(-12*x)/12 | exponential | x |
atom-0590 | atomic | 1 | -4*exp(-5*x) | - 4 e^{- 5 x} | \int - 4 e^{- 5 x} \, dx | 4*exp(-5*x)/5 | exponential | x |
atom-0591 | atomic | 1 | 4*exp(15*x) | 4 e^{15 x} | \int 4 e^{15 x} \, dx | 4*exp(15*x)/15 | exponential | x |
atom-0592 | atomic | 1 | -5*exp(5*x) | - 5 e^{5 x} | \int - 5 e^{5 x} \, dx | -exp(5*x) | exponential | x |
atom-0593 | atomic | 1 | exp(-2*x) | e^{- 2 x} | \int e^{- 2 x} \, dx | -exp(-2*x)/2 | exponential | x |
atom-0594 | atomic | 1 | exp(7*x) | e^{7 x} | \int e^{7 x} \, dx | exp(7*x)/7 | exponential | x |
atom-0595 | atomic | 1 | -exp(-12*x) | - e^{- 12 x} | \int - e^{- 12 x} \, dx | exp(-12*x)/12 | exponential | x |
atom-0596 | atomic | 1 | exp(-15*x) | e^{- 15 x} | \int e^{- 15 x} \, dx | -exp(-15*x)/15 | exponential | x |
atom-0597 | atomic | 1 | -2*exp(8*x) | - 2 e^{8 x} | \int - 2 e^{8 x} \, dx | -exp(8*x)/4 | exponential | x |
atom-0598 | atomic | 1 | 4*exp(4*x) | 4 e^{4 x} | \int 4 e^{4 x} \, dx | exp(4*x) | exponential | x |
atom-0599 | atomic | 1 | -4*exp(-11*x) | - 4 e^{- 11 x} | \int - 4 e^{- 11 x} \, dx | 4*exp(-11*x)/11 | exponential | x |
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