difficulty
stringclasses 3
values | category
stringclasses 6
values | question
stringlengths 5
35
|
|---|---|---|
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
|
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