Advanced Math Calculators

Solve complex integrals, derivatives, and differential equations with step-by-step solutions.

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Integral Calculator

Solve definite and indefinite integrals with step-by-step solutions.
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  • Basic integration formulas: ∫xndx=xn+1n+1+C\int x^n dx = \frac{x^{n+1}}{n+1} + C
  • Sum and difference rule, Constant multiple rule
  • Substitution rule (uu-substitution)
  • Integration by parts: ∫u dv=uv−∫v du\int u \, dv = uv - \int v \, du
  • Integration of rational functions
  • Method of undetermined coefficients
  • Ostrogradsky-Hermite method
  • Euler substitutions
  • Fundamental Theorem of Calculus
  • Improper integrals
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Derivative Calculator

Find derivatives of functions with detailed steps.
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  • Common derivatives: xx, sin⁡(x)\sin(x), cos⁡(x)\cos(x), tan⁡(x)\tan(x), exe^x, ln⁡(x)\ln(x)
  • Constant rule, Constant multiple rule, Sum/Difference rule
  • Power rule: ddx[xn]=nxn−1\frac{d}{dx}[x^n] = n x^{n-1}
  • Product rule: (uv)′=u′v+uv′(uv)' = u'v + uv'
  • Quotient rule: (uv)′=u′v−uv′v2\left(\frac{u}{v}\right)' = \frac{u'v - uv'}{v^2}
  • Reciprocal rule, Chain rule
  • Implicit differentiation
  • Higher-order derivatives (f′′(x)f''(x), f′′′(x)f'''(x))
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Limit Calculator

Calculate limits of functions as they approach a specific value.
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  • Limit of a constant, Sum/Product/Quotient rules
  • Common limits: lim⁡x→0sin⁡(x)x=1\lim_{x \to 0} \frac{\sin(x)}{x} = 1
  • Squeeze theorem
  • L'Hôpital's rule
  • Taylor series expansions
  • One-sided limits (left and right-hand limits)
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Equation Solver

Solve algebraic equations, quadratics, and systems of equations.
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  • Determining the domain
  • Linear and Quadratic equations
  • Cubic & Quartic equations (Ferrari's method)
  • Factoring rational roots
  • Roots of complex numbers
  • Half-angle tangent substitution
  • Binomial theorem and Polynomial identities
  • Complex logarithms
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ODE Solver

Solve ordinary differential equations step-by-step.
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  • Separable equations, Homogeneous equations
  • First-order linear equations
  • Bernoulli equations, Riccati equations
  • Exact differential equations, Integrating factors
  • Linear differential equations with constant coefficients
  • Cauchy-Euler equations
  • Systems of linear equations
  • Initial Value Problems (IVP)
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Complex Numbers

Calculate with imaginary numbers and phases.
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  • Algebraic form: z=a+biz = a + bi
  • Trigonometric form, Exponential form
  • Modulus, Root, and Power
  • Rationalizing a fraction by its conjugate
  • Complex logarithm

Popular Topics

Indefinite Integral Definite Integral Integration by Parts U-Substitution Partial Fractions Chain Rule Product Rule Implicit Differentiation L'Hôpital's Rule Limits at Infinity Quadratic Equations System of Equations Laplace Transform Taylor Series Differential Equations (ODE)