Integral of $$$1512 x$$$

Find $$$\int 1512 x\, dx$$$.

Apply the constant multiple rule $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ with $$$c=1512$$$ and $$$f{\left(x \right)} = x$$$:

$${\color{red}{\int{1512 x d x}}} = {\color{red}{\left(1512 \int{x d x}\right)}}$$

Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=1$$$:

$$1512 {\color{red}{\int{x d x}}}=1512 {\color{red}{\frac{x^{1 + 1}}{1 + 1}}}=1512 {\color{red}{\left(\frac{x^{2}}{2}\right)}}$$

Therefore,

$$\int{1512 x d x} = 756 x^{2}$$

Add the constant of integration:

$$\int{1512 x d x} = 756 x^{2}+C$$

$$$\int 1512 x\, dx = 756 x^{2} + C$$$A