Math Lab

🔢 Math Operations

Equation or Expression:

Use ** for powers (e.g., x**2), * for multiplication (e.g., 3*x)

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Variable:

Syntax Guide:

Enter a polynomial equation in one variable, equated to zero.
Use ** for powers (e.g., x**4), * for multiplication (e.g., 3*x).
Examples: x**2 + 3*x - 4 = 0, x**4 + 1 = 0

For Best Results:

Only single-variable polynomials are supported for root-finding.
Very high degree polynomials may be slow or have complex roots.

Differential Equation:

Use prime notation: y', y'', y''', y''''

Differential Equation Format:

First-order: y' = x**2 - x**5
Higher-order (≤4): y'' = x**2 or y''' + 2*y'' + y' = sin(x)
Incorrect: dy/dx = x**2 - x**5 (use y' instead)
Incorrect: x**2 - x**5 (missing derivative and equals sign)

Performance Tips:

Start with simpler equations: y' = x**2 before y'' = exp(-x)*sin(x)*tan(x)

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Independent Variable:

Solution Constants:

Constants will be automatically generated when plotting.

Expression to Integrate:

Quick Select:

Tips for Complex Integrals:

For complex expressions like sin(x)*log(x)-x^9, use definite integrals with specific bounds
Expressions with nested functions may fall back to numerical integration
For better performance, split complex integrals into simpler terms

Variable:

Type:

Integration Syntax:

⚠️ Expression Grouping Warning: Use parentheses to group expressions correctly. For example:
x**3/(x-3)*(x+5) ≠ x**3/((x-3)*(x+5))
The first evaluates as (x³/(x-3))×(x+5), while the second evaluates as x³/((x-3)×(x+5)).

Expression for Derivative:

Derivative Input Guide:

Explicit: x**2 - x**5 + sin(x) (computes df/dx)
Implicit: x**2 + y**2 = 25 (computes dy/dx)
Incorrect: dy/dx = x**2 - x**5
Incorrect: x**2 - x**5 = 0 (use for algebraic solving)

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Variable:

Order:

Enable Extended Analysis Shows detailed tangent line calculations at additional points

Additional Tangent Line at x = Tangent lines at critical points are shown automatically

f(x): Use SymPy notation: x**2, exp(x), sin(x), log(x)

α — exponent in (1+x)^α:

Expansion point a:

Number of terms:

x min:

x max: