difficulty stringclasses 3
values | category stringclasses 6
values | question stringlengths 5 35 |
|---|---|---|
Moderate | Trigonometric Substitution | ∫√6+9y2dy |
Advanced | Trigonometric Substitution | ∫(1−8z2)32dz |
Moderate | Trigonometric Substitution | ∫√9−16(3x−1)2dx |
Moderate | Trigonometric Substitution | ∫(11+(t2+1)2)52dt |
Advanced | Trigonometric Substitution | ∫√144(z+8)2−3dz |
Moderate | Trigonometric Substitution | ∫√4x2−24x+43dx |
Moderate | Trigonometric Substitution | ∫(2z2−24z+36)112dz |
Moderate | Trigonometric Substitution | ∫√−4−10t−5t2dt |
Moderate | Trigonometric Substitution | ∫√9sin2(4t)−1dt |
Moderate | Trigonometric Substitution | ∫√36−9e3zdz |
Advanced | Trigonometric Substitution | ∫√x+16dx |
Moderate | Trigonometric Substitution | ∫3x5√16−x2dx |
Advanced | Trigonometric Substitution | ∫t3(25+81t2)52dt |
Advanced | Trigonometric Substitution | ∫140w3√1−9w2dw |
Advanced | Trigonometric Substitution | ∫z5(9z2−25)32dz |
Moderate | Trigonometric Substitution | ∫−1−3y3√49y2−4dy |
Moderate | Trigonometric Substitution | ∫515x2√x2+4dx |
Advanced | Trigonometric Substitution | ∫√3−4t2t2dt |
Moderate | Trigonometric Substitution | ∫w5√8w2+1dw |
Advanced | Trigonometric Substitution | ∫√x2−15x3dx |
Moderate | Trigonometric Substitution | ∫2(x−3)6√−x2+6x−5dx |
Moderate | Trigonometric Substitution | ∫1(z+1)2(2z2+4z−34)32dz |
Moderate | Trigonometric Substitution | ∫√4y2−16y+19(y−2)6dy |
Advanced | Trigonometric Substitution | ∫129(t−4)3√t2−8t+7dt |
Moderate | Trigonometric Substitution | ∫60√5x2+10x+6dx |
Moderate | Trigonometric Substitution | ∫x7√9−x4dx |
Advanced | Trigonometric Substitution | ∫e12t√4e6t−1dt |
Advanced | Trigonometric Substitution | ∫sin(z)cos3(z)√16+cos2(z)dz |
Advanced | Multiple Integrals | ∫∞0(1+2x)e−xdx |
Advanced | Multiple Integrals | ∫0−∞(1+2x)e−xdx |
Moderate | Multiple Integrals | ∫1−5110+2zdz |
Moderate | Multiple Integrals | ∫214w3√w2−4dw |
Moderate | Multiple Integrals | ∫1−∞√6−ydy |
Moderate | Multiple Integrals | ∫∞29(1−3z)4dz |
Basic | Multiple Integrals | ∫40xx2−9dx |
Basic | Multiple Integrals | ∫∞−∞6w3(w4+1)2dw |
Basic | Multiple Integrals | ∫411x2+x−6dx |
Moderate | Multiple Integrals | ∫0−∞e1xx2dx |
Advanced | Multiple Integrals | ∫∞42−4x+6x2dx |
Advanced | Multiple Integrals | ∫5014w−20dw |
Advanced | Multiple Integrals | ∫2−136√4−2zdz |
Moderate | Multiple Integrals | ∫0−∞xe2+3xdx |
Moderate | Multiple Integrals | ∫∞0xe2+3xdx |
Advanced | Multiple Integrals | ∫∞21x2+1dx |
Advanced | Multiple Integrals | ∫301z2−4zdz |
Moderate | Multiple Integrals | ∫1−∞xx2+1dx |
Advanced | Multiple Integrals | ∫2−11y2−2y−3dy |
Moderate | Multiple Integrals | ∫0−∞cos(w)dw |
Moderate | Multiple Integrals | ∫∞101(5−2z)2dz |
Moderate | Multiple Integrals | ∫∞−∞z3z4+1dz |
Moderate | Multiple Integrals | ∫4112y−6dy |
Moderate | Multiple Integrals | ∫5113√w−2dw |
Advanced | Multiple Integrals | ∫1−2e1xx2dx |
Advanced | Multiple Integrals | ∫∞−∞x2ex3dx |
Advanced | Multiple Integrals | ∫∞−∞y(y2+1)3dy |
Moderate | Multiple Integrals | ∫30w3√9−w2dw |
Advanced | Multiple Integrals | ∫1−31w2+2wdw |
Advanced | Multiple Integrals | ∫∞0e1xx2dx |
Moderate | Multiple Integrals | ∫∞01z[ln(z)]2dz |
Moderate | Multiple Integrals | ∫∞01w−1dw |
Basic | Partial Fractions | ∫sin3(23x)cos4(23x)dx |
Basic | Partial Fractions | ∫sin8(3z)cos5(3z)dz |
Moderate | Partial Fractions | ∫cos4(2t)dt |
Advanced | Partial Fractions | ∫2ππcos3(12w)sin5(12w)dw |
Basic | Partial Fractions | ∫sec6(3y)tan2(3y)dy |
Advanced | Partial Fractions | ∫tan3(6x)sec10(6x)dx |
Basic | Partial Fractions | ∫π40tan7(z)sec3(z)dz |
Basic | Partial Fractions | ∫cos(3t)sin(8t)dt |
Advanced | Partial Fractions | ∫31sin(8x)sin(x)dx |
Moderate | Partial Fractions | ∫cot(10z)csc4(10z)dz |
Moderate | Partial Fractions | ∫csc6(14w)cot4(14w)dw |
Moderate | Partial Fractions | ∫sec4(2t)tan9(2t)dt |
Basic | Partial Fractions | ∫2+7sin3(z)cos2(z)dz |
Basic | Partial Fractions | ∫[9sin5(3x)−2cos3(3x)]csc4(3x)dx |
Moderate | Trigonometric Substitution | ∫cos5(2t)sin2(2t)dt |
Advanced | Trigonometric Substitution | ∫cos3(12x)dx |
Advanced | Trigonometric Substitution | ∫cos2(z)sin4(z)dz |
Advanced | Trigonometric Substitution | ∫ππ3sin5(34w)cos6(34w)dw |
Advanced | Trigonometric Substitution | ∫π0cos11(5z)sin3(5z)dz |
Moderate | Trigonometric Substitution | ∫sin2(7x)dx |
Moderate | Trigonometric Substitution | ∫π60tan3(8x)sec3(8x)dx |
Moderate | Trigonometric Substitution | ∫sec8(12t)tan5(12t)dt |
Advanced | Trigonometric Substitution | ∫sec2(9z)tan3(9z)dz |
Advanced | Trigonometric Substitution | ∫π3π4sec6(10t)tan4(10t)dt |
Moderate | Trigonometric Substitution | ∫tan12(2w)sec6(2w)dw |
Moderate | Trigonometric Substitution | ∫cot2(3x)csc6(3x)dx |
Advanced | Trigonometric Substitution | ∫2π3π3csc3(14w)cot3(14w)dw |
Advanced | Trigonometric Substitution | ∫csc4(6w)dw |
Moderate | Trigonometric Substitution | ∫csc12(x)cot5(x)dx |
Moderate | Trigonometric Substitution | ∫cot(x)dx |
Moderate | Trigonometric Substitution | ∫cot3(x)dx |
Moderate | Trigonometric Substitution | ∫csc(x)dx |
Advanced | Trigonometric Substitution | ∫csc3(x)dx |
Moderate | Trigonometric Substitution | ∫4−2sin(8x)cos(15x)dx |
Advanced | Trigonometric Substitution | ∫cos(2x)cos(24x)dx |
Moderate | Trigonometric Substitution | ∫sin(13z)sin(9z)dz |
Moderate | Trigonometric Substitution | ∫cos5(2t)sin3(2t)dt |
Moderate | Trigonometric Substitution | ∫sin3(2−x)cos2(2−x)dx |
Moderate | Trigonometric Substitution | ∫sec6(12z)tan8(12z)dz |
Moderate | Trigonometric Substitution | ∫tan5(x)sec2(x)dx |
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