Home › Calculus › Antiderivative and integral
  • Antiderivative and integral
  • Definite integral
  • Improper integrals
  • Double integrals
  • Triple integrals
  • Line integrals
  • Surface integrals
  • Elements of field theory
  • Bringing a factor under the differential sign
  • Tangent line equations
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  1. Antiderivative of f(x) = x² cos x³.
  2. Antiderivative of f(x) = sin³ x.
  3. Antiderivative of f(x) = x · e²ˣ.
  4. Antiderivative of f(x) = x · ln 2x.
  5. Antiderivative of f(x) = x · cos 3x.
  6. Antiderivative of f(x) = arccos 3x.
  1. Definite integral (2x+3)/(x²+3x+2).
  2. Definite integral x/(x+1)².
  3. Definite integral 1/(x²−2x+5).
  4. Definite integral ctg³x.
  5. Definite integral cos³x·sin⁴x.
  6. Definite integral x/(1+√(x+1)).
  1. Improper integral arccos(1/x)/(x√x).
  2. Improper integral (√x+x²)/(x²+x³+5).
  3. Improper integral dx/ln²x.
  4. Improper integral arctg(x²/(x+1))/(x²+4).
  1. Mass of a plane figure between y = 8 − x² and y = x + 2.
  2. Area between the parabolas.
  3. Volume of a body under a paraboloid in a cylinder.
  1. Triple integral (x²+y²) in the cylinder x²+y² = −2x.
  2. Mass of a tetrahedron with density ρ = 24xyz.
  3. Triple integral (x²+y²+z²) over a ball.
  1. Line integral x dy − y dx along the parabola y = x³.
  2. Line integral x dy − y dx along a circle.
  3. Line integral z dl / √(x²+y²) along a helix.
  1. Surface integral x dS over a conical surface.
  2. Surface integral z dS over the plane z = 1.
  3. Flux of the second kind over a hemisphere of radius 1.
  4. Flux of the second kind over a paraboloid.
  1. Curl of a vector field.
  2. Divergence of a vector field.
  3. Gradient of a scalar field.
  1. Bringing under the differential sign.
  1. Tangent line equations to a function graph.
  1. Linear equations.
  2. Quadratic equations.
  3. Irrational equations.
  4. Exponential equations.
  5. Logarithmic equations.
  6. Trigonometric equations.
  1. Calculations and transformations.
  2. Equations.
  3. Word problems.
  4. Geometry.
  1. Algebra.
  2. Geometry.
  3. Real-life mathematics.