Mw
backToHome

Integral com Passos Explicativos

Gratuito · Privado · Roda no seu navegador — sem necessidade de cadastro

Looking for related tools? Try our derivative calculator with steps, our limit calculator with steps, or our multiple integral calculator.

Sem servidor⚡ Web Worker
∫ Integral
Tipo de Integral
Amostras Demonstrativas:
Teclado Matemático
Chargement du clavier…

Estruturas Triviais.

1) Direcionamento Original Lógico.

  • A Regra da Potência:
    ∫xn dx=xn+1n+1+C\int x^n \, dx = \frac{x^{n+1}}{n+1} + C
  • Constante Básica:
    ∫c dx=cx+C\int c \, dx = cx + C
  • Multiplicador de Constante Interna Analítica e Oficial Resultante Extensivo.:
    ∫cf(x) dx=c∫f(x) dx\int c f(x) \, dx = c \int f(x) \, dx

2) Funções Categóricas e Extensões Exóticas

  • ∫sin⁡(x) dx=−cos⁡(x)+C\int \sin(x) \, dx = -\cos(x) + C
  • ∫cos⁡(x) dx=sin⁡(x)+C\int \cos(x) \, dx = \sin(x) + C
  • ∫ex dx=ex+C\int e^x \, dx = e^x + C
  • ∫1x dx=ln⁡∣x∣+C\int \frac{1}{x} \, dx = \ln|x| + C
Chargement du graphique…
∫

Digite a expressão e pressione Ir

A Arte da Integração: Acumulando Valor

O processo de encontrar o total de uma quantidade variável com soluções exatas.

A Regra da Potência

∫xn dx=xn+1n+1+C\int x^n \, dx = \frac{x^{n+1}}{n+1} + C

A regra fundamental para funções polinomiais.

u-Substitution

∫f(g(x))g′(x) dx=F(g(x))+C\int f(g(x))g'(x)\,dx = F(g(x)) + C

Transforms composite integrals by substituting u = g(x).

Fundamental Theorem

∫abf(x) dx=F(b)−F(a)\int_a^b f(x)\,dx = F(b) - F(a)

Links antiderivatives to the area under a curve.

Como a Integração Funciona

Em física e engenharia, é usada para deduções exatas de cálculos acumulativos.

Integrais Definidas vs. Indefinidas

Integrais Indefinidas

Apresentam a família de primitivas e incluem a constante de integração C.

∫f(x) dx=F(x)+C\int f(x) \, dx = F(x) + C

Integrais Definidas

Apresentam área estrita delimitada.

∫abf(x) dx=F(b)−F(a)\int_{a}^{b} f(x) \, dx = F(b) - F(a)

Regras Padrão de Integração e Diferenciação

A Regra da Potência

∫xn dx=xn+1n+1+C\int x^n \, dx = \frac{x^{n+1}}{n+1} + C

A regra fundamental para funções polinomiais.

Exponenciais

∫ex dx=ex+C\int e^x \, dx = e^x + C

A base dos modelos de crescimento.

Perguntas Frequentes

Lida com derivadas secundárias e terciárias?

Sim! Você pode calcular ordens superiores.

Os resultados são precisos e perfeitos?

O motor algébrico fornece a precisão simbólica exata e confiável.

How do you solve an integral with steps?

Identify whether the integral is indefinite or definite, then choose the right technique: apply the power rule for polynomials, u-substitution for composite functions, integration by parts for products, or trigonometric identities for trig expressions. For definite integrals, evaluate the antiderivative at both bounds and subtract.

What integration techniques does this calculator support?

Mathsway supports the Power Rule, u-Substitution, Integration by Parts, Trigonometric Integration, Partial Fractions, and standard exponential and logarithmic integral formulas — all with full algebraic steps.

What is the difference between definite and indefinite integrals?

An indefinite integral finds the general antiderivative F(x) + C, representing a family of functions. A definite integral evaluates the accumulated area between a function and the x-axis over a specific interval [a, b], yielding a numerical result via the Fundamental Theorem of Calculus.

How does u-substitution work?

U-substitution is the integral counterpart of the Chain Rule. You substitute u = g(x) to transform a complex integral into a simpler one in terms of u. After integrating, substitute back to express the result in terms of x.

Is this integral calculator free and does it require signup?

Yes, it is completely free, runs directly in your browser with Web Workers, requires no account or signup, and your data remains private on your device.

How are integrals related to derivatives?

By the Fundamental Theorem of Calculus, integration and differentiation are inverse operations. The derivative of an antiderivative gives back the original function. You can verify your work step by step with our derivative calculator with steps.

Can this calculator solve improper integrals?

Improper integrals involve infinite bounds or discontinuous integrands and are evaluated as limits. This calculator focuses on standard definite and indefinite integrals with step-by-step solutions. For limit evaluation, you can also use our limit calculator with steps.