Para resolver sua questão, devemos aplicar a substituição simples. Chamando então:
[tex]\large\displaystyle\text{$\begin{aligned} \int \sin (4x+2) dx \Rightarrow \begin{cases} u = 4x+2\\ du = 4\ dx\\ dx = \frac{du}{4}\end{cases} \end{aligned}$}[/tex]
[tex]\large\displaystyle\text{$\begin{aligned} \int \sin (4x+2) dx = \int \sin ( u) \frac{du}{4} \end{aligned}$}[/tex]
[tex]\large\displaystyle\text{$\begin{aligned} \int \sin (4x+2) dx = \frac{1}{4} \int \sin ( u) du \end{aligned}$}[/tex]
[tex]\large\displaystyle\text{$\begin{aligned} \int \sin (4x+2) dx = \frac{1}{4} \cdot -\cos (u) + k\end{aligned}$}[/tex]
[tex]\large\displaystyle\text{$\begin{aligned} \int \sin (4x+2) dx = -\frac{1}{4} \cos (u) + k\end{aligned}$}[/tex]
Substitua agora o u por 4x + 2. Ficando assim:
[tex]\large\displaystyle\text{$\begin{aligned} \int \sin (4x+2) dx = -\frac{1}{4} \cos (u) + k\end{aligned}$}[/tex]
[tex]\large\displaystyle\text{$\begin{aligned} \therefore \boxed{\boxed{\green{\int \sin (4x+2) dx = -\frac{1}{4} \cos (4x+2) + k}}}\end{aligned}$}[/tex]
Integrais indefinidas.
[tex]\blue{\square}[/tex] brainly.com.br/tarefa/5929110
