Symbolic algebra

Choose an operation, type an expression, and press Enter (or Compute). Implicit multiplication works (3x^2, 2sin(x)); use ^ for powers, e, pi, and i for the constants, and log(x) for the natural logarithm.
Solve accepts an equation (x^3 - 6x^2 + 11x = 6) or an expression taken as = 0, for the variable you name (default: x). Solve system takes one linear equation per line.
Differentiate takes an order; Integrate is indefinite unless you give both limits (-Infinity and Infinity work); Limit accepts Infinity or -Infinity; Taylor series expands to the order you give about any point (computed from successive derivatives).
Substitute replaces variables with values or other expressions (a = 2, b = x+1) and tidies the result; Evaluate numerically gives a decimal.
Command passes anything straight to the engine, for example laplace(t^2, t, s), ilt(1/(s^2+1), s, t), sum(k^2, k, 1, 10), determinant(matrix([1,2],[3,4])), or gcd(x^2-1, x^2-2x+1).
Each result is a step: Use puts it back in the input, Plot draws it, and LaTeX or Text copy it. Download .tex exports the whole history as a LaTeX document.

The engine is nerdamer 1.1.13; maths is typeset with KaTeX. Both load from jsdelivr on first use. Like any CAS it can fail to find an antiderivative or a closed-form root that exists, and simplification is not canonical — check important results numerically (the ≈ line and the plot help).

Step-by-step working for linear equations, inequalities, quadratics and polynomial division: algebra step by step.

Share link (under the title) copies a URL that reopens this tool exactly as you have it — every tab’s inputs, with the current tab selected. Opening such a link replaces the inputs this browser had saved for the tool.

Linking to an example

Companion to chapters 16–19 (limits, derivatives, their applications, and integrals) of Mathematics, Reconnected. A link opens the tool with an expression and an operation and computes it at once, adding a step to your history. Write one by hand, for example /tools/cas/?expr=x^2*sin(x)&op=integrate or ?expr=sin(x)/x&op=limit&at=0.

Parameter Meaning Example

Parameter	Meaning	Example
`expr`	the expression, equation or (for `system`) equations separated by `;`	`expr=x^3-2x-5=0`
`op`	`simplify`, `expand`, `factor`, `solve`, `system`, `diff`, `integrate`, `limit`, `taylor`, `partfrac`, `subst`, `evaluate`, or `raw`	`op=diff`
`var`	the variable (default: x, or t)	`var=t`
`order`	derivative order or Taylor order	`order=3`
`from`, `to`	limits of a definite integral (`-Infinity`, `Infinity`, `pi` work)	`from=0&to=pi`
`at`	the point for a limit or Taylor series	`at=Infinity`
`values`	for `subst` and `evaluate`: `name = value` pairs	`values=a=2,b=-3`
`plot`	expressions for the plot, separated by `;`	`plot=sin(x);x`
`example`	one of the presets below; other parameters override it	`example=ch19-parts`

expr

the expression, equation or (for system) equations separated by ;

expr=x^3-2x-5=0

op

simplify, expand, factor, solve, system, diff, integrate, limit, taylor, partfrac, subst, evaluate, or raw

op=diff

var

the variable (default: x, or t)

var=t

order

derivative order or Taylor order

order=3

from, to

limits of a definite integral (-Infinity, Infinity, pi work)

from=0&to=pi

at

the point for a limit or Taylor series

at=Infinity

values

for subst and evaluate: name = value pairs

values=a=2,b=-3

plot

expressions for the plot, separated by ;

plot=sin(x);x

example

one of the presets below; other parameters override it

example=ch19-parts

In expr, from, to, at, values and plot a ` typed into the address means plus (`?expr=x^2+1`); a value fully percent-encoded (spaces as `%20` or `, plus as %2B) is read exactly as encoded, so links copied with Share link keep working.

Presets:

ch16-limit-factor — lim x→3 of (x² − 9)/(x² − x − 6) = 6/5 (cancel the common factor)
ch16-limit-cubic — lim x→1 of (x³ − 1)/(x − 1) = 3
ch16-limit-root — lim x→0 of (√(x + 9) − 3)/x = 1/6 (rationalise)
ch16-limit-sin3x — lim x→0 of sin(3x)/x = 3
ch16-limit-cos — lim x→0 of (1 − cos x)/x = 0
ch17-power-rule — d/dx of 4x⁵ − 3x² + 2/x − 7√x + 9
ch17-product-rule — d/dx of x² sin x
ch17-quotient-rule — d/dx of x/(x² + 1)
ch17-chain-rule — d/dx of (3x² + 1)⁵
ch17-chain-three — d/dx of sin³(2x), three layers
ch17-arctan — d/dx of arctan x = 1/(1 + x²)
ch18-cubic — f(x) = x³ − 3x² − 9x + 5: f′ and its zeros
ch18-cubic-critical — Critical points: solve 3x² − 6x − 9 = 0
ch18-box — Open box: dV/dx for V = x(20 − 2x)²
ch18-taylor-sin — Taylor series of sin x about 0
ch19-ftc-parabola — ∫₀² x² dx = 8/3
ch19-ftc-poly — ∫₁³ (3x² − 4x + 5) dx = 20
ch19-substitution — ∫ 2x cos(x²) dx = sin(x²) + C
ch19-substitution-log — ∫ x/(x² + 1) dx
ch19-substitution-limits — ∫₀¹ x(x² + 1)³ dx = 15/8
ch19-parts — ∫ x eˣ dx by parts
ch19-parts-log — ∫ ln x dx
ch19-partfrac — Partial fractions of 1/(x² − 1)
ch19-improper — ∫₀¹ 1/√x dx = 2

Related: graphing calculator (sliders, roots, shaded integrals), algebra step by step.

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Linking to an example