Input syntax & keys
/ fraction, ^ exponent, _ log base, ( | brackets
build structure as you type
Tab or → accepts a suggestion, e.g.
arcs → arcsin(▢)autocomplete
← → ↑ ↓, Tab, Space leaves an exponent
move between slots
Function names are colored by rule family: trig inverse trig exp & log hyperbolic inverse hyp. roots & abs
color key
x^2, x**2, x²powers
2x, x sin x, (x+1)(x-1)implicit multiplication
sin x^2 = sin(x²), sin^2 x = (sin x)²function notation
sin^-1 x, arcsin, asininverse functions
sqrt(x), cbrt(x), √xroots
e^x, exp(x), ln x, log x (base 10), log_2(x), log(b, x)exponentials & logs
|x|, abs(x)absolute value
pi, π, e; other letters like a, kconstants
sinh cosh tanh coth sech csch, arsinh…hyperbolic
Techniques the integrator uses
x^5, 1/x, e^(3x), sec x tan x, 1/(x^2+4)table of common integrals
x cos(x^2), (ln x)/x, x sqrt(x+1)u-substitution
x e^x, ln x, x^2 arctan x, e^x sin xintegration by parts (LIATE, cyclic)
(x^3+1)/(x^2+1), 1/(x^2(x+1)), 1/(x^2+2x+5)division, partial fractions, completing the square
sin^3 x, cos^2 x, sec^3 x, sin(3x)cos(2x)trig powers, half-angle, reduction, product-to-sum
sqrt(1-x^2), sqrt(x^2+1), 1/(x^2+1)^2trigonometric substitution
1/(1+cos x), 1/(2+sin x)tangent half-angle substitution
Input works the same as for derivatives: / fraction, ^ exponent, Tab autocomplete
input
Rule Library
Every rule the solver uses, with its proof. Click a rule to read it.
Proof Map
Each arrow points from a result to a rule proved using it. Everything flows from the ε–δ definition of a limit. Hover a rule to trace what it depends on and what depends on it; click it to read the proof.