difficulty
stringclasses 3
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35
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|---|---|---|
Advanced | Integration by Parts | ∫
xtan(x)
cos2(x)
dx |
Advanced | Integration by Parts | ∫
xsin2(x)cot2(x)
cos4(x)
dx |
Advanced | Integration by Parts | ∫xsin(3x)cos(2x)dx |
Advanced | Integration by Parts | ∫x2sin(x)cos(x)dx |
Moderate | Integration by Parts | ∫4xcos(2−3x)dx |
Advanced | Integration by Parts | ∫06(2+5x)e13xdx |
Advanced | Integration by Parts | ∫(3t+t2)sin(2t)dt |
Moderate | Integration by Parts | ∫6tan−1(8w)dw |
Moderate | Integration by Parts | ∫e2zcos(14z)dz |
Advanced | Integration by Parts | ∫π0x2cos(4x)dx |
Moderate | Integration by Parts | ∫t7sin(2t4)dt |
Advanced | Integration by Parts | ∫y6cos(3y)dy |
Moderate | Integration by Parts | ∫(4x3−9x2+7x+3)e−xdx |
Advanced | Multiple Integrals | ∫−21∫0√4−y2xy2dxdy |
Advanced | Multiple Integrals | ∫02∫ y 1x2ydxdy |
Advanced | Multiple Integrals | ∫01∫01xydxdy |
Advanced | Multiple Integrals | ∫03∫023x2y3dxdy |
Advanced | Multiple Integrals | ∫04∫15(y2+3x2)dxdy |
Advanced | Multiple Integrals | ∫12∫01x2ydxdy |
Advanced | Multiple Integrals | ∫04∫04e(4x+5y)dxdy |
Advanced | Multiple Integrals | ∫02π∫0√5√4+r2rdrdθ |
Advanced | Multiple Integrals | ∫0 π ∫01+cos(θ)sin(θ)rrdrdθ |
Advanced | Multiple Integrals | ∫02π∫01∫44r2cos(θ)r2dzdrdθ |
Advanced | Multiple Integrals | ∫02∫y22y∫−√z√zxdxdzdy |
Advanced | Multiple Integrals | ∫02π∫01∫9r28−9r2r2dzdrdθ |
Advanced | Multiple Integrals | ∫02π∫0 ∫04−9r2r2dzdrdθ |
Advanced | Multiple Integrals | ∫04∫−44∫0y21dzdydx |
Advanced | Multiple Integrals | ∫02π∫1√2∫r2−r2(2−2r2)rdzdrdθ |
Advanced | Multiple Integrals | ∫0π∫01∫0−(−1+r)r2zdzdrdθ |
Advanced | Multiple Integrals | ∫01∫√z1∫zx2(5+4x)dydxdz |
Advanced | Multiple Integrals | ∫01∫0ln(8)∫0ln(16)30e−x−y−zdzdydx |
Advanced | Multiple Integrals | ∫02π∫00.4636∫02sin(φ)p2dpdφdθ |
Moderate | Integration by Parts | ∫8te7tdt∫8te7tdt |
Advanced | Integration by Parts | ∫2ππ(1−3x)sin(12x)dx |
Advanced | Integration by Parts | ∫2−1w2e4wdw |
Moderate | Integration by Parts | ∫31(2−x)2ln(4x)dx |
Advanced | Integration by Parts | ∫(6+3z)cos(1+4z)dz |
Moderate | Integration by Parts | ∫2y2cos(9y)dy |
Moderate | Integration by Parts | ∫(3z+z2)sin(z)dz |
Moderate | Integration by Parts | ∫√x3ln(3√x)dx |
Moderate | Integration by Parts | ∫(2w2−w)e7w−1dw |
Advanced | Integration by Parts | ∫9tsec2(2t)dt |
Advanced | Integration by Parts | ∫π80e−xsin(4x)dx |
Advanced | Integration by Parts | ∫8tan−1(2y)dy |
Advanced | Integration by Parts | ∫e6tcos(2t)dt |
Advanced | Integration by Parts | ∫−3sin−1(10x)dx |
Moderate | Integration by Parts | ∫e3−zsin(2+z)dz |
Moderate | Integration by Parts | ∫0−12x17e1+x9dx |
Moderate | Integration by Parts | ∫9t11cos(1−t6)dt |
Moderate | Integration by Parts | ∫x7√x4+1dx |
Moderate | Integration by Parts | ∫(5+x4)sin(12x)dx |
Advanced | Integration by Parts | ∫2z5e1−zdz |
Advanced | Integration by Parts | ∫(5+2w3−w5)cos(3w)dw |
Advanced | Partial Fractions | ∫9z2−12zdz |
Advanced | Partial Fractions | ∫7xx2+14x+40dx |
Advanced | Partial Fractions | ∫408y−12y2−15y−8dy |
Advanced | Partial Fractions | ∫9−w2(w+1)(3w−5)(w+4)dw |
Moderate | Partial Fractions | ∫8112z3−2z2−63zdz |
Moderate | Partial Fractions | ∫7x+2x2(x−4)(2x+3)(2x+1)dx |
Moderate | Partial Fractions | ∫4x+10(x−2)(x−1)2dx |
Moderate | Partial Fractions | ∫2124t4−6t3dt |
Moderate | Partial Fractions | ∫10z+2(z+1)2(z−3)2dz |
Advanced | Partial Fractions | ∫8w+w2(w−7)(w2+16)dw |
Moderate | Partial Fractions | ∫6y−7(2y+1)(4y2+1)dy |
Moderate | Partial Fractions | ∫8t3−5t2+72t−10(t2+2)(t2+9)dt |
Advanced | Partial Fractions | ∫16w3+6w2+12w+21(w2+9)(4w2+3)dw |
Moderate | Partial Fractions | ∫x4+5x3+20x+16x(x2+4)2dx |
Moderate | Partial Fractions | ∫6−z22z2+z−21dz |
Moderate | Partial Fractions | ∫4x3−xx2−x−30dx |
Moderate | Partial Fractions | ∫8−t3(t−3)(t+1)2dt |
Moderate | Partial Fractions | ∫x6−6x5+3x4−10x3−9x2+12x−27x4+3x2dx |
Moderate | Partial Fractions | ∫4x2+5x−14dx |
Moderate | Partial Fractions | ∫8−3t10t2+13t−3dt |
Moderate | Partial Fractions | ∫0−1w2+7w(w+2)(w−1)(w−4)dw |
Moderate | Partial Fractions | ∫83x3+7x2+4xdx |
Moderate | Partial Fractions | ∫423z2+1(z+1)(z−5)2dz |
Advanced | Partial Fractions | ∫4x−11x3−9x2dx |
Advanced | Partial Fractions | ∫z2+2z+3(z−6)(z2+4)dz |
Moderate | Partial Fractions | ∫8+t+6t2−12t3(3t2+4)(t2+7)dt |
Advanced | Partial Fractions | ∫6x2−3x(x−2)(x+4)dx |
Moderate | Partial Fractions | ∫2+w4w3+9wdw |
Moderate | Trigonometric Substitution | ∫√4−9z24dz |
Advanced | Trigonometric Substitution | ∫√13+25x213+25x2dx |
Moderate | Trigonometric Substitution | ∫(7t2−3)52dt |
Advanced | Trigonometric Substitution | ∫√4(9t−5)2+14(9t−5)2+1dt |
Advanced | Trigonometric Substitution | ∫√1−4z−2z2dz |
Advanced | Trigonometric Substitution | ∫(x2−8x+21)32dx |
Advanced | Trigonometric Substitution | ∫√e8x−9dx |
Advanced | Trigonometric Substitution | ∫√x2+16x4dx |
Advanced | Trigonometric Substitution | ∫√1−7w2dw |
Moderate | Trigonometric Substitution | ∫t3(3t2−4)52dt |
Moderate | Trigonometric Substitution | ∫−5−72y4√y2−25dy |
Moderate | Trigonometric Substitution | ∫412z5√2+9z2dz |
Moderate | Trigonometric Substitution | ∫1√9x2−36x+37dx |
Advanced | Trigonometric Substitution | ∫(z+3)5(40−6z−z2)32dz |
Advanced | Trigonometric Substitution | ∫cos(x)√9+25sin2(x)dx |
Moderate | Trigonometric Substitution | ∫√64t2+164t2+1dt |
Moderate | Trigonometric Substitution | ∫√4z2−49dz |
Moderate | Trigonometric Substitution | ∫√7−w2dw |
Moderate | Trigonometric Substitution | ∫(16−81x2)72dx |
Subsets and Splits