Calculator Guide

Symbolic algebra

Symbolic expressions use free variables instead of only numbers. When an expression contains a symbol, Hissab keeps the result algebraic, collects like terms, and returns a simplified expression.

12 + 2x^2 - 4x^2 - 2
(x + 2)*(x + 3)
derivative(2x^2, x)
integrate(2x^2 + 3x + 10, x)
limit(sin(x)/x, x, 0)

Symbols

The recognized free variables are x, y, and z. Other identifiers are treated as unknown words and make the expression invalid.

3x - 10y + 13z
x*y + 2x

Implicit multiplication works between a number and a symbol, so 2x means 2*x. Use an explicit operator between symbols: write x*y or x y, not xy.

Simplify and expand

A bare expression with symbols is simplified automatically. simplify(...) is the explicit form.

12 + 2x^2 - 4x^2 - 2
simplify(2x^2 - 4x^2)
(x + 1)*(x + 2)
(x + 1)*(x + 1)

Hissab returns canonical polynomial output ordered by descending degree.

Derivatives

Use derivative(expr, variable). diff is an alias.

derivative(2x^2, x)
diff(sin(x), x)
derivative(x^2*y, x)

With more than one symbol, the variable argument chooses the partial derivative.

Integrals

Use integrate(expr, variable). integral is an alias. Definite integrals add lower and upper bounds.

integrate(2x^2 + 3x + 10, x)
integral(2x^2 + 3x + 10, x)
integrate(2x^2 + 3x + 10, x, 0, 50)

The constant of integration is omitted for indefinite integrals.

Limits

Use limit(expr, variable, point).

limit(4x^2 - 3x + 10, x, 0)
limit(sin(x)/x, x, 0)

When a derivative, integral, or limit has no closed form, Hissab may return a numeric estimate for limits and definite integrals. An indefinite integral with no elementary antiderivative is left in integral form.

Common mistakes