Integral de $$$a_{n} i_{n} + b_{n} i_{n} + 1$$$ em relação a $$$x$$$

Encontre $$$\int \left(a_{n} i_{n} + b_{n} i_{n} + 1\right)\, dx$$$.

Aplique a regra da constante $$$\int c\, dx = c x$$$ usando $$$c=a_{n} i_{n} + b_{n} i_{n} + 1$$$:

$${\color{red}{\int{\left(a_{n} i_{n} + b_{n} i_{n} + 1\right)d x}}} = {\color{red}{x \left(a_{n} i_{n} + b_{n} i_{n} + 1\right)}}$$

Portanto,

$$\int{\left(a_{n} i_{n} + b_{n} i_{n} + 1\right)d x} = x \left(a_{n} i_{n} + b_{n} i_{n} + 1\right)$$

Adicione a constante de integração:

$$\int{\left(a_{n} i_{n} + b_{n} i_{n} + 1\right)d x} = x \left(a_{n} i_{n} + b_{n} i_{n} + 1\right)+C$$

$$$\int \left(a_{n} i_{n} + b_{n} i_{n} + 1\right)\, dx = x \left(a_{n} i_{n} + b_{n} i_{n} + 1\right) + C$$$A