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-0400 | atomic | 1 | -exp(7*x) | - e^{7 x} | \int - e^{7 x} \, dx | -exp(7*x)/7 | exponential | x |
atom-0401 | atomic | 1 | 4*exp(-6*x) | 4 e^{- 6 x} | \int 4 e^{- 6 x} \, dx | -2*exp(-6*x)/3 | exponential | x |
atom-0402 | atomic | 1 | 2*exp(-9*x) | 2 e^{- 9 x} | \int 2 e^{- 9 x} \, dx | -2*exp(-9*x)/9 | exponential | x |
atom-0403 | atomic | 1 | -4*exp(-x) | - 4 e^{- x} | \int - 4 e^{- x} \, dx | 4*exp(-x) | exponential | x |
atom-0404 | atomic | 1 | 2*exp(-13*x) | 2 e^{- 13 x} | \int 2 e^{- 13 x} \, dx | -2*exp(-13*x)/13 | exponential | x |
atom-0405 | atomic | 1 | 5*exp(-4*x) | 5 e^{- 4 x} | \int 5 e^{- 4 x} \, dx | -5*exp(-4*x)/4 | exponential | x |
atom-0406 | atomic | 1 | 3*exp(2*x) | 3 e^{2 x} | \int 3 e^{2 x} \, dx | 3*exp(2*x)/2 | exponential | x |
atom-0407 | atomic | 1 | -exp(12*x) | - e^{12 x} | \int - e^{12 x} \, dx | -exp(12*x)/12 | exponential | x |
atom-0408 | atomic | 1 | 5*exp(-10*x) | 5 e^{- 10 x} | \int 5 e^{- 10 x} \, dx | -exp(-10*x)/2 | exponential | x |
atom-0409 | atomic | 1 | 3*exp(-8*x) | 3 e^{- 8 x} | \int 3 e^{- 8 x} \, dx | -3*exp(-8*x)/8 | exponential | x |
atom-0410 | atomic | 1 | -2*exp(10*x) | - 2 e^{10 x} | \int - 2 e^{10 x} \, dx | -exp(10*x)/5 | exponential | x |
atom-0411 | atomic | 1 | 2*exp(-15*x) | 2 e^{- 15 x} | \int 2 e^{- 15 x} \, dx | -2*exp(-15*x)/15 | exponential | x |
atom-0412 | atomic | 1 | 4*exp(-4*x) | 4 e^{- 4 x} | \int 4 e^{- 4 x} \, dx | -exp(-4*x) | exponential | x |
atom-0413 | atomic | 1 | 3*exp(-11*x) | 3 e^{- 11 x} | \int 3 e^{- 11 x} \, dx | -3*exp(-11*x)/11 | exponential | x |
atom-0414 | atomic | 1 | -4*exp(-13*x) | - 4 e^{- 13 x} | \int - 4 e^{- 13 x} \, dx | 4*exp(-13*x)/13 | exponential | x |
atom-0415 | atomic | 1 | 2*exp(x) | 2 e^{x} | \int 2 e^{x} \, dx | 2*exp(x) | exponential | x |
atom-0416 | atomic | 1 | exp(11*x) | e^{11 x} | \int e^{11 x} \, dx | exp(11*x)/11 | exponential | x |
atom-0417 | atomic | 1 | -3*exp(-5*x) | - 3 e^{- 5 x} | \int - 3 e^{- 5 x} \, dx | 3*exp(-5*x)/5 | exponential | x |
atom-0418 | atomic | 1 | 2*exp(-x) | 2 e^{- x} | \int 2 e^{- x} \, dx | -2*exp(-x) | exponential | x |
atom-0419 | atomic | 1 | -3*exp(13*x) | - 3 e^{13 x} | \int - 3 e^{13 x} \, dx | -3*exp(13*x)/13 | exponential | x |
atom-0420 | atomic | 1 | 3*exp(5*x) | 3 e^{5 x} | \int 3 e^{5 x} \, dx | 3*exp(5*x)/5 | exponential | x |
atom-0421 | atomic | 1 | -3*exp(-2*x) | - 3 e^{- 2 x} | \int - 3 e^{- 2 x} \, dx | 3*exp(-2*x)/2 | exponential | x |
atom-0422 | atomic | 1 | -5*exp(11*x) | - 5 e^{11 x} | \int - 5 e^{11 x} \, dx | -5*exp(11*x)/11 | exponential | x |
atom-0423 | atomic | 1 | -3*exp(-6*x) | - 3 e^{- 6 x} | \int - 3 e^{- 6 x} \, dx | exp(-6*x)/2 | exponential | x |
atom-0424 | atomic | 1 | -2*exp(-4*x) | - 2 e^{- 4 x} | \int - 2 e^{- 4 x} \, dx | exp(-4*x)/2 | exponential | x |
atom-0425 | atomic | 1 | 3*exp(13*x) | 3 e^{13 x} | \int 3 e^{13 x} \, dx | 3*exp(13*x)/13 | exponential | x |
atom-0426 | atomic | 1 | -4*exp(-7*x) | - 4 e^{- 7 x} | \int - 4 e^{- 7 x} \, dx | 4*exp(-7*x)/7 | exponential | x |
atom-0427 | atomic | 1 | 3*exp(-7*x) | 3 e^{- 7 x} | \int 3 e^{- 7 x} \, dx | -3*exp(-7*x)/7 | exponential | x |
atom-0428 | atomic | 1 | -exp(4*x) | - e^{4 x} | \int - e^{4 x} \, dx | -exp(4*x)/4 | exponential | x |
atom-0429 | atomic | 1 | 4*exp(-11*x) | 4 e^{- 11 x} | \int 4 e^{- 11 x} \, dx | -4*exp(-11*x)/11 | exponential | x |
atom-0430 | atomic | 1 | 4*exp(8*x) | 4 e^{8 x} | \int 4 e^{8 x} \, dx | exp(8*x)/2 | exponential | x |
atom-0431 | atomic | 1 | 4*exp(-14*x) | 4 e^{- 14 x} | \int 4 e^{- 14 x} \, dx | -2*exp(-14*x)/7 | exponential | x |
atom-0432 | atomic | 1 | -5*exp(-13*x) | - 5 e^{- 13 x} | \int - 5 e^{- 13 x} \, dx | 5*exp(-13*x)/13 | exponential | x |
atom-0433 | atomic | 1 | 5*exp(9*x) | 5 e^{9 x} | \int 5 e^{9 x} \, dx | 5*exp(9*x)/9 | exponential | x |
atom-0434 | atomic | 1 | 5*exp(-9*x) | 5 e^{- 9 x} | \int 5 e^{- 9 x} \, dx | -5*exp(-9*x)/9 | exponential | x |
atom-0435 | atomic | 1 | exp(4*x) | e^{4 x} | \int e^{4 x} \, dx | exp(4*x)/4 | exponential | x |
atom-0436 | atomic | 1 | 2*exp(13*x) | 2 e^{13 x} | \int 2 e^{13 x} \, dx | 2*exp(13*x)/13 | exponential | x |
atom-0437 | atomic | 1 | -exp(5*x) | - e^{5 x} | \int - e^{5 x} \, dx | -exp(5*x)/5 | exponential | x |
atom-0438 | atomic | 1 | 2*exp(-8*x) | 2 e^{- 8 x} | \int 2 e^{- 8 x} \, dx | -exp(-8*x)/4 | exponential | x |
atom-0439 | atomic | 1 | 5*exp(-3*x) | 5 e^{- 3 x} | \int 5 e^{- 3 x} \, dx | -5*exp(-3*x)/3 | exponential | x |
atom-0440 | atomic | 1 | -4*exp(7*x) | - 4 e^{7 x} | \int - 4 e^{7 x} \, dx | -4*exp(7*x)/7 | exponential | x |
atom-0441 | atomic | 1 | 2*exp(-2*x) | 2 e^{- 2 x} | \int 2 e^{- 2 x} \, dx | -exp(-2*x) | exponential | x |
atom-0442 | atomic | 1 | -2*exp(-5*x) | - 2 e^{- 5 x} | \int - 2 e^{- 5 x} \, dx | 2*exp(-5*x)/5 | exponential | x |
atom-0443 | atomic | 1 | exp(-11*x) | e^{- 11 x} | \int e^{- 11 x} \, dx | -exp(-11*x)/11 | exponential | x |
atom-0444 | atomic | 1 | -2*exp(-x) | - 2 e^{- x} | \int - 2 e^{- x} \, dx | 2*exp(-x) | exponential | x |
atom-0445 | atomic | 1 | -5*exp(-6*x) | - 5 e^{- 6 x} | \int - 5 e^{- 6 x} \, dx | 5*exp(-6*x)/6 | exponential | x |
atom-0446 | atomic | 1 | 4*exp(-2*x) | 4 e^{- 2 x} | \int 4 e^{- 2 x} \, dx | -2*exp(-2*x) | exponential | x |
atom-0447 | atomic | 1 | -3*exp(11*x) | - 3 e^{11 x} | \int - 3 e^{11 x} \, dx | -3*exp(11*x)/11 | exponential | x |
atom-0448 | atomic | 1 | -3*exp(x) | - 3 e^{x} | \int - 3 e^{x} \, dx | -3*exp(x) | exponential | x |
atom-0449 | atomic | 1 | -exp(-15*x) | - e^{- 15 x} | \int - e^{- 15 x} \, dx | exp(-15*x)/15 | exponential | x |
atom-0450 | atomic | 1 | exp(x) | e^{x} | \int e^{x} \, dx | exp(x) | exponential | x |
atom-0451 | atomic | 1 | -2*exp(-9*x) | - 2 e^{- 9 x} | \int - 2 e^{- 9 x} \, dx | 2*exp(-9*x)/9 | exponential | x |
atom-0452 | atomic | 1 | -5*exp(-14*x) | - 5 e^{- 14 x} | \int - 5 e^{- 14 x} \, dx | 5*exp(-14*x)/14 | exponential | x |
atom-0453 | atomic | 1 | 4*exp(13*x) | 4 e^{13 x} | \int 4 e^{13 x} \, dx | 4*exp(13*x)/13 | exponential | x |
atom-0454 | atomic | 1 | 5*exp(-6*x) | 5 e^{- 6 x} | \int 5 e^{- 6 x} \, dx | -5*exp(-6*x)/6 | exponential | x |
atom-0455 | atomic | 1 | -4*exp(-2*x) | - 4 e^{- 2 x} | \int - 4 e^{- 2 x} \, dx | 2*exp(-2*x) | exponential | x |
atom-0456 | atomic | 1 | -exp(8*x) | - e^{8 x} | \int - e^{8 x} \, dx | -exp(8*x)/8 | exponential | x |
atom-0457 | atomic | 1 | exp(-4*x) | e^{- 4 x} | \int e^{- 4 x} \, dx | -exp(-4*x)/4 | exponential | x |
atom-0458 | atomic | 1 | -5*exp(3*x) | - 5 e^{3 x} | \int - 5 e^{3 x} \, dx | -5*exp(3*x)/3 | exponential | x |
atom-0459 | atomic | 1 | 3*exp(-6*x) | 3 e^{- 6 x} | \int 3 e^{- 6 x} \, dx | -exp(-6*x)/2 | exponential | x |
atom-0460 | atomic | 1 | 3*exp(-x) | 3 e^{- x} | \int 3 e^{- x} \, dx | -3*exp(-x) | exponential | x |
atom-0461 | atomic | 1 | -exp(11*x) | - e^{11 x} | \int - e^{11 x} \, dx | -exp(11*x)/11 | exponential | x |
atom-0462 | atomic | 1 | 5*exp(4*x) | 5 e^{4 x} | \int 5 e^{4 x} \, dx | 5*exp(4*x)/4 | exponential | x |
atom-0463 | atomic | 1 | -4*exp(-3*x) | - 4 e^{- 3 x} | \int - 4 e^{- 3 x} \, dx | 4*exp(-3*x)/3 | exponential | x |
atom-0464 | atomic | 1 | 3*exp(15*x) | 3 e^{15 x} | \int 3 e^{15 x} \, dx | exp(15*x)/5 | exponential | x |
atom-0465 | atomic | 1 | -3*exp(-9*x) | - 3 e^{- 9 x} | \int - 3 e^{- 9 x} \, dx | exp(-9*x)/3 | exponential | x |
atom-0466 | atomic | 1 | -5*exp(-11*x) | - 5 e^{- 11 x} | \int - 5 e^{- 11 x} \, dx | 5*exp(-11*x)/11 | exponential | x |
atom-0467 | atomic | 1 | 4*exp(-5*x) | 4 e^{- 5 x} | \int 4 e^{- 5 x} \, dx | -4*exp(-5*x)/5 | exponential | x |
atom-0468 | atomic | 1 | -5*exp(-4*x) | - 5 e^{- 4 x} | \int - 5 e^{- 4 x} \, dx | 5*exp(-4*x)/4 | exponential | x |
atom-0469 | atomic | 1 | 5*exp(-15*x) | 5 e^{- 15 x} | \int 5 e^{- 15 x} \, dx | -exp(-15*x)/3 | exponential | x |
atom-0470 | atomic | 1 | -exp(15*x) | - e^{15 x} | \int - e^{15 x} \, dx | -exp(15*x)/15 | exponential | x |
atom-0471 | atomic | 1 | 4*exp(3*x) | 4 e^{3 x} | \int 4 e^{3 x} \, dx | 4*exp(3*x)/3 | exponential | x |
atom-0472 | atomic | 1 | -2*exp(-14*x) | - 2 e^{- 14 x} | \int - 2 e^{- 14 x} \, dx | exp(-14*x)/7 | exponential | x |
atom-0473 | atomic | 1 | -4*exp(-9*x) | - 4 e^{- 9 x} | \int - 4 e^{- 9 x} \, dx | 4*exp(-9*x)/9 | exponential | x |
atom-0474 | atomic | 1 | -2*exp(-2*x) | - 2 e^{- 2 x} | \int - 2 e^{- 2 x} \, dx | exp(-2*x) | exponential | x |
atom-0475 | atomic | 1 | 4*exp(14*x) | 4 e^{14 x} | \int 4 e^{14 x} \, dx | 2*exp(14*x)/7 | exponential | x |
atom-0476 | atomic | 1 | -5*exp(7*x) | - 5 e^{7 x} | \int - 5 e^{7 x} \, dx | -5*exp(7*x)/7 | exponential | x |
atom-0477 | atomic | 1 | -2*exp(2*x) | - 2 e^{2 x} | \int - 2 e^{2 x} \, dx | -exp(2*x) | exponential | x |
atom-0478 | atomic | 1 | 5*exp(x) | 5 e^{x} | \int 5 e^{x} \, dx | 5*exp(x) | exponential | x |
atom-0479 | atomic | 1 | -3*exp(-x) | - 3 e^{- x} | \int - 3 e^{- x} \, dx | 3*exp(-x) | exponential | x |
atom-0480 | atomic | 1 | 3*exp(-4*x) | 3 e^{- 4 x} | \int 3 e^{- 4 x} \, dx | -3*exp(-4*x)/4 | exponential | x |
atom-0481 | atomic | 1 | 5*exp(5*x) | 5 e^{5 x} | \int 5 e^{5 x} \, dx | exp(5*x) | exponential | x |
atom-0482 | atomic | 1 | -2*exp(-7*x) | - 2 e^{- 7 x} | \int - 2 e^{- 7 x} \, dx | 2*exp(-7*x)/7 | exponential | x |
atom-0483 | atomic | 1 | -2*exp(15*x) | - 2 e^{15 x} | \int - 2 e^{15 x} \, dx | -2*exp(15*x)/15 | exponential | x |
atom-0484 | atomic | 1 | -exp(9*x) | - e^{9 x} | \int - e^{9 x} \, dx | -exp(9*x)/9 | exponential | x |
atom-0485 | atomic | 1 | -2*exp(7*x) | - 2 e^{7 x} | \int - 2 e^{7 x} \, dx | -2*exp(7*x)/7 | exponential | x |
atom-0486 | atomic | 1 | 2*exp(-4*x) | 2 e^{- 4 x} | \int 2 e^{- 4 x} \, dx | -exp(-4*x)/2 | exponential | x |
atom-0487 | atomic | 1 | -exp(-6*x) | - e^{- 6 x} | \int - e^{- 6 x} \, dx | exp(-6*x)/6 | exponential | x |
atom-0488 | atomic | 1 | 5*exp(2*x) | 5 e^{2 x} | \int 5 e^{2 x} \, dx | 5*exp(2*x)/2 | exponential | x |
atom-0489 | atomic | 1 | -4*exp(-4*x) | - 4 e^{- 4 x} | \int - 4 e^{- 4 x} \, dx | exp(-4*x) | exponential | x |
atom-0490 | atomic | 1 | 5*exp(-7*x) | 5 e^{- 7 x} | \int 5 e^{- 7 x} \, dx | -5*exp(-7*x)/7 | exponential | x |
atom-0491 | atomic | 1 | -exp(14*x) | - e^{14 x} | \int - e^{14 x} \, dx | -exp(14*x)/14 | exponential | x |
atom-0492 | atomic | 1 | -exp(-11*x) | - e^{- 11 x} | \int - e^{- 11 x} \, dx | exp(-11*x)/11 | exponential | x |
atom-0493 | atomic | 1 | 4*exp(-8*x) | 4 e^{- 8 x} | \int 4 e^{- 8 x} \, dx | -exp(-8*x)/2 | exponential | x |
atom-0494 | atomic | 1 | 5*exp(13*x) | 5 e^{13 x} | \int 5 e^{13 x} \, dx | 5*exp(13*x)/13 | exponential | x |
atom-0495 | atomic | 1 | 5*exp(-8*x) | 5 e^{- 8 x} | \int 5 e^{- 8 x} \, dx | -5*exp(-8*x)/8 | exponential | x |
atom-0496 | atomic | 1 | exp(-5*x) | e^{- 5 x} | \int e^{- 5 x} \, dx | -exp(-5*x)/5 | exponential | x |
atom-0497 | atomic | 1 | -4*exp(6*x) | - 4 e^{6 x} | \int - 4 e^{6 x} \, dx | -2*exp(6*x)/3 | exponential | x |
atom-0498 | atomic | 1 | -5*exp(15*x) | - 5 e^{15 x} | \int - 5 e^{15 x} \, dx | -exp(15*x)/3 | exponential | x |
atom-0499 | atomic | 1 | 2*exp(5*x) | 2 e^{5 x} | \int 2 e^{5 x} \, dx | 2*exp(5*x)/5 | exponential | x |
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