Decompose rational expressions into partial fractions. Handles distinct linear, repeated linear, and irreducible quadratic factors. Shows every algebraic step for integration prep.
Find inflection points using the second derivative test with full sign-change verification, concavity intervals, and complete step-by-step working. Not just root-finding — genuine concavity change confirmed.
Solve first-order ordinary differential equations with initial conditions. Handles separable, linear, and exact ODEs. Shows complete integration and constant-finding steps.
Free inverse Laplace transform calculator. Find ℒ⁻¹{F(s)} = f(t) via direct table lookup or partial fraction decomposition — with complete step-by-step working for polynomials, exponentials, trig, and damped oscillations
Find dy/dx for any implicit equation, evaluate at a point, find tangent lines, and compute second derivatives d²y/dx².
chain rule calculator with full step-by-step decomposition into outer f(u) and inner g(x) functions. Solves single-variable, nested triple composition, and multivariable chain rule with partial derivatives. Instant results with verification
Find the indefinite integral of any function polynomials, trig, exponentials, logarithms with complete step-by-step working showing every integration rule applied and automatic verification.
Calculate partial derivatives of multivariable functions with respect to x, y, or z. Finds first and second partial derivatives, mixed partials, and gradient vector with full steps.
Triple integral calculator with coordinate converter (Cartesian, cylindrical, spherical), volume integral calculator for 3D shapes, Jacobian calculator, and integration limits reference.
Create frequency distribution tables from raw data. Calculates class width, relative frequency, cumulative frequency, and generates histogram data. Shows mean,
median, and mode from grouped data.