Integral de $$$30 x$$$

Encontre $$$\int 30 x\, dx$$$.

Aplique a regra do múltiplo constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ usando $$$c=30$$$ e $$$f{\left(x \right)} = x$$$:

$${\color{red}{\int{30 x d x}}} = {\color{red}{\left(30 \int{x d x}\right)}}$$

Aplique a regra da potência $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ com $$$n=1$$$:

$$30 {\color{red}{\int{x d x}}}=30 {\color{red}{\frac{x^{1 + 1}}{1 + 1}}}=30 {\color{red}{\left(\frac{x^{2}}{2}\right)}}$$

Portanto,

$$\int{30 x d x} = 15 x^{2}$$

Adicione a constante de integração:

$$\int{30 x d x} = 15 x^{2}+C$$

$$$\int 30 x\, dx = 15 x^{2} + C$$$A