Eneontive a Primitiva de funço f(x) = 4x + 4x^3 (x pertence a R)

Passo 1

Beleza, vamos lá! A questão pede para encontrar a primitiva da função . Isso está dentro do assunto de cálculo, mais especificamente de integrais e primitivas. Para resolver isso, vamos precisar saber como integrar funções polinomiais usando a regra do poder.

Passo 2

Primeiro, vamos lembrar que a primitiva de uma função é basicamente a antiderivada dela. Ou seja, se é a primitiva de , então .

Passo 3

Vamos quebrar a função em duas partes para facilitar a integração:

Passo 4

Agora, aplicamos a regra do poder para integrar cada termo. A regra do poder diz que:
onde é a constante de integração.

Passo 5

Aplicando a regra do poder ao primeiro termo :

Passo 6

Agora, aplicamos a mesma regra ao segundo termo :

Passo 7

Juntando os dois resultados e adicionando a constante de integra��ão :

Resposta

A primitiva de é:

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Windoo Método de Exaustäa de Arquímeder, eneontre , ande 0 < a < b.
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Usando a Té́miea de Mudança de variável, encentre .
Entregar ressolvida em folla de Papel A^4 em 1210812024.